Ok ... yes she will be a dependent up until the age of 24 if she is still in school.  As for the 529 plan withdrawls  ... they should be done in her name up to the standard deduction for the year.  For instance if she takes out $12K then the same amount of the scholarship will be taxable on her return however she will owe no taxes or penalties.  You can do this every year she is in college to drain the account tax free. 

Q. I have read that I can withdraw up to the scholarship amount per calendar year without having to pay the 10% penalty - is that so?

A. Yes.  The earnings portion of the distribution (withdrawal amount) will still be taxable, but there will be no penalty.

Q. Assuming it is, how will this be reflected on the tax forms?

A. The taxable portion of the 529 distribution (the earnings) will be reported on line 8 of Schedule 1 with the notation Taxable portion of 1099-Q (or similar wording).  There is a line on form 5329 to claim the penalty exception.  TurboTax (TT) can handle this, but it can get a little tricky.  It's helpful if you know what the expected outcome is (so, you've asked good questions).

Q.  I assume my financial institution (529 plan administrator) will see the withdrawal and send me a tax form?

A. Yes, form 1099-Q.

Q.  How will the plan administrator  know that the penalty is not applicable?  

A.  They won't and they don't care.  They only report what's required on form 1099-Q (total distribution, broken down between earning and basis).  It's your job to tell the IRS you have a penalty exception. 

Q. Can I still show her as a dependent given she has no income in 2021? 

A.  Yes.  Scholarships are ignored in the dependent support test.  That is, she is not considered to be supporting her self (it's essentially third party support). So, she can continue to be treated as a qualifying child dependent through age 23, if a full time student.  Even though she will be reporting scholarship as income (and maybe some 529 earnings), those are not considered self support, for purposes of the  qualifying child dependent  support test

@Critter-3  said "As for the 529 plan withdrawals; they should be done in her name"

That is generally true, but it can get complicated.  The only way to be sure is prepare trial returns both ways and compare. You may actually want to distribute some of the money to the student and some to the parent. The earnings portion of a 529 distribution is unearned income and subject to the "kiddie tax".  As such, a "child" under 24 (whether a dependent or not) will not be allowed a full $12, 550 (2021) standard deduction.  But, the room and board portion  of the scholarship will also be taxable income to the student.  Taxable scholarship is treated as earned income for purposes of calculating a student's standard deduction, so she will be allowed the standard deduction to cover (up to $12,550) of the taxable scholarship. 

@Critter-3  said "For instance if she takes out $12K then the same amount of the scholarship will be taxable on her return"

The amount of scholarship that is taxable is not related to the 529 distribution amount *. Only the amount of the scholarship used for qualified expenses (tuition, fees and required course materials) is tax free.  The rest (mostly the room and board part) is taxable.

* The amount of distribution that is penalty free is related to the scholarship amount). 

Qualified Tuition Plans  (QTP 529 Plans) Distributions

General Discussion 

It’s complicated.

For 529 plans, there is an “owner” (usually the parent), and a “beneficiary” (usually the student dependent). The "recipient" of the distribution can be either the owner or the beneficiary depending on who the money was sent to. When the money goes directly from the Qualified Tuition Plan (QTP) to the school, the student is the "recipient". The distribution will be reported on IRS form 1099-Q. 
The 1099-Q gets reported on the recipient's return.** The recipient's name & SS# will be on the 1099-Q.
Even though the 1099-Q is going on the student's return, the 1098-T should go on the parent's return, so you can claim the education credit. You can do this because he is your dependent.

You can and should claim the tuition credit before claiming the 529 plan earnings exclusion. The educational expenses he claims for the 1099-Q should be reduced by the amount of educational expenses you claim for the credit.
But be aware, you can not double dip. You cannot count the same tuition money, for the tuition credit,  that gets him an exclusion from the taxability of the earnings (interest) on the 529 plan. Since the credit is more generous; use as much of the tuition as is needed for the credit and the rest for the interest exclusion. Another special rule allows you to claim the tuition credit even though it was "his" money that paid the tuition.
In addition, there is another rule that says the 10% penalty is waived if he was unable to cover the 529 plan withdrawal with educational expenses either because he got scholarships or the expenses were used (by him or the parents) to claim the credits. He'll have to pay tax on the earnings, at his lower tax rate (subject to the “kiddie tax”), but not the penalty.

Total qualified expenses (including room & board) less amounts paid by scholarship less amounts used to claim the Tuition credit equals the amount you can use to claim the earnings exclusion on the 1099-Q. 
Example:
  $10,000 in educational expenses(including room & board)

   -$3000 paid by tax free scholarship***

   -$4000 used to claim the American Opportunity credit

 =$3000 Can be used against the 1099-Q (usually on the student’s return)

Box 1 of the 1099-Q is $5000

Box 2 is $2800

3000/5000=60% of the earnings are tax free; 40% are taxable

40% x 2800= $1120

You have $1120 of taxable income  

**Alternatively; you can just not report the 1099-Q, at all, if your student-beneficiary has sufficient educational expenses, including room & board (even if he lives at home) to cover the distribution. You would still have to do the math to see if there were enough expenses left over for you to claim the tuition credit. Again, you cannot double dip!  When the box 1 amount on form 1099-Q is fully covered by expenses, TurboTax will enter nothing about the 1099-Q on the actual tax forms. But, it will prepare a 1099-Q worksheet for your records, in case of an IRS inquiry.

On form 1099-Q, instructions to the recipient reads: "Nontaxable distributions from CESAs and QTPs are not required to be reported on your income tax return. You must determine the taxability of any distribution." 

***Another alternative is have the student report some of his scholarship as taxable income, to free up some expenses for the 1099-Q and/or tuition credit. Most people come out better having the scholarship taxable before the 529 earnings. 

One more thing:  Student is getting a free ride, so that appears to mean that the parent can't claim a tuition credit.

But, there is a tax “loop hole” available. The student reports all his scholarship, up to the amount needed to claim the American Opportunity Credit (AOC), as income on his return. That way, the parents  (or himself, if he is not a dependent) can claim the tuition credit on their return. They can do this because that much tuition was no longer paid by "tax free" scholarship.  You cannot do this if the school’s billing statement specifically shows the scholarships being applied to tuition or if the conditions of the grant are that it be used to pay for qualified expenses.

Using an example: Student has $10,000 in box 5 of the 1098-T and $8000 in box 1. At first glance he/she has $2000 of taxable income and nobody can claim the American opportunity credit. But if she reports $6000 as income on her return, the parents can claim $4000 of qualified expenses on their return.

Wow, thank you SO MUCH for your responses. To simply this a bit, my employment income is too high for taking tuition credit or American Opportunity credit so I don't need to worry about that. However, I had no idea that:

- The scholarship is a taxable income. Will I receive a tax form for that from her college? 

- Part of the income could be allocated to her (for the obvious reason she has never filed a tax return). 

Given we may decide to experiment with two tax returns (hers in addition to mine), does it matter who the distribution goes to? Obviously, the easiest way for me to just send money to my personal bank account and figure out the rest later, but maybe it needs to go to her right away to be able to show this as her income? 

Last question for now: how do I determine how much I can withdraw from 529 account? Here are some rough numbers:

Full cost of her attending this college is $75,000

Her scholarship is $81,000

She started as a freshman in August'21

How much can I withdraw in 2021 without incurring a penalty? I assume it is not the entire $81K because her scholarship is for the entire 21/22 school year? 

I've always done my taxes myself, but sounds like I may need an accountant this year... Still would like to understand fundamentals here before I hire someone. Thanks again for your help!

Q.  The scholarship is a taxable income. Will I receive a tax form for that from her college? 

A.  Yes, but not specifically for only the taxable portion.  The form is 1098-T.  Box 1 is tuition and fees and box 5 scholarships. Put simply, the difference between box 5 and box 1 is the taxable amount.  But that taxable amount can be reduced by the cost of any required course materials (books and computers and software). 

Q. Does it matter who the 529 distribution goes to? 

A. Yes, See the general discussion above. The "recipient" reports the 529 earnings income on their tax return.  

Q. How much can I withdraw in 2021 without incurring a penalty? I assume it is not the entire $81K because her scholarship is for the entire 21/22 school year? 

A. Correct, it's not the full $$75K  (full cost of attending college).  You don't go by the $81K (unless the extra $6K is something that 529 money is allowed to be used for, such as books).   I suspect it's simply half the $75K, if the school is a typical 2 semester school with the first semester ending in 2021.  The school should be able to tell you for sure.  You can add up front costs (typically purchasing a computer).