I have 3 interest bearing accounts with the same bank. I did not receive any 1099s. Can I combine the accounts into one box for reporting interest or do I need to list each account's interest separately?

yes. 

Yes you can enter the Total of all accounts for the same bank.   Maybe you can log into your bank account and download the 1099 pdf or even import it.  Banks should have the 1099 tax statements listed online.  I would assume if you have 3 accounts the total interest its over $10?   

Enter a 1099-Int under

Federal

Wages & Income

Interest and Dividends

Interest on 1099-INT - Click the Start or Update button

Put the total amount in Box 1

Don't try to import it. On the Let Us Enter Your 1099 page scroll down to the bottom and pick Enter a different way

Yes, since the three accounts are at the same bank, you can combine the interest amounts into one entry.

Here's how to enter that in TurboTax:

1. Sign in to TurboTax.
2. Select Income & Expenses.
3. Select Start or Update to the right of Investments and Savings (1099-B, 1099-INT, 1099-DIV, 1099-K, Crypto).
4. Answer the first question Yes, or if you already have some income here, select Add investment.
5. Select Enter a different way.
6. Select the Interest tile and Continue.
7. Select Type it in myself at the bottom.
8. Enter the bank's name.
9. Enter your income in box 1 or 3 as it is on the 1099-INT.
10. If you have other boxes filled in on your 1099-INT, check the box next to My form has info in other boxes (this is uncommon).
11. Complete the rest of the form, then Continue.
12. Answer the remaining questions based on your situation. 
     

Thank you for your answers! They did answer my question. 

I realized after making the post that we do have another savings account with the same bank, but it is only in my wife's name.  Since it asks who the account belongs to, I interpret that to mean that that account's interest would have to be entered as a separate 1099-INT (I did not receive any 1099-INT forms at all for any of the accounts). Am I correct?

Thank you again.

Yes, add the interest from your account and make one pseudo 1099-INT and then enter another one for your spouse.

Great! Thank you for your time and attention!