On your Form W4, you normally put the number of exemptions you claim on your Tax Return, which in your case is 1 (yourself), so that is correct.  

On your Tax Return, you claim your Exemption amount but don't list yourself as a "Dependent" since you are the Taxpayer.  It is assumed that you are claiming yourself (meaning taking your Exemption) unless you check the box that indicates you are "a dependent of another."

If this doesn't clear up your question, please comment below so I can assist you further.

So it is okay to add myself as a dependent on my W4 form?

Its my first job and I live alone and pay for everything myself.

You do not claim yourself as a dependent on your tax return.   You can only claim someone ELSE as a dependent on your tax return.   Your W-4 does not go to the IRS.   Your W-4 only goes to your employer so that the employer knows how much tax to withhold from your paychecks.   If you do not have enough withheld, then you could owe tax when you prepare your tax return.   If you have more than your tax liability withheld, then you get a refund.

https://ttlc.intuit.com/community/tax-topics/help/what-to-know-about-the-new-2020-irs-form-w-4-emplo...

https://www.irs.gov/pub/irs-pdf/fw4.pdf

https://www.irs.gov/individuals/tax-withholding-estimator