My dependents are not in the Choose a name dropdown menu, but they are already verified dependents in the dependent area. If I click Add Another Person, they're listed.

Dependents are not the same as qualifying relatives. I am going to assume this is for college entries where things can get blurry or a technical issue.

1.Students under the age of 24, full time in school, usually qualify to be dependents rather than qualifying relatives, perhaps your children are not dependents this year.

See  Publication 501 - Internal Revenue Service page 11 to verify that you qualify to claim the dependent or if they are in fact, a qualifying relative.

 

2. Another option is that you have some piece of data stuck. Follow these steps:

Online version:

A full or corrupted cache can cause problems in TurboTax, so sometimes you need to clear your cache (that is, remove these temporary files).

For stuck information follow these steps:

1. Delete the form/ worksheet with dropdown issue- if possible, see How to Delete  
2. Log out of your return and try one or more of the following:
   • Don't use Internet Explorer.
   • Clear cache and cookies,
   • Sign in using a different browser.
   • Sign in using a different device.
3. Log back into your return.
   • Enter the information again.

 

Desktop version: 

1. Delete the form/ area with dropdown issue
2. Save your return while closing the program.
3. Update the program
4. Open
5. Enter the information again.

 

If this does not answer your question, please reply with more information and the area of your return.