You do not have a choice about whether or not you can be claimed as a dependent. There is a fixed set of tests to determine whether or not you can be claimed as a dependent. If you meet all the tests you can be claimed as a dependent. If you do not meet all the tests, you cannot be claimed as a dependent. You must file your tax return in accordance with the results of the tests that determine whether or not you can be claimed as a dependent. It's not something you can choose.
Having student loans, or making payments on student loans, does not affect whether or not you can be claimed as a dependent. That's not one of the tests.
The rules for determining whether or not someone can be claimed as a dependent are described in detail in the Dependents section of IRS Publication 501, pages 10 through 22 (in the 2018 edition). The publication is written from the point of view of the person who might be able to claim the dependent, not from the point of view of the person who might be claimed as a dependent. You will also see that there are actually two sets of tests, for two different types of dependents. If you meet either set of tests you can be claimed as a dependent. You can download Publication 501 from the following link.
https://www.irs.gov/pub/irs-pdf/p501.pdf
I am not aware of any situation in which your student loan payment amounts would be affected by whether or not you can be claimed as a dependent. But that is not a question of tax law. If you want to be certain, ask the lender or servicer of your student loans. It might be particularly advisable to ask about it if you are in an income-based repayment program.
