If I take money out of my trust, then pay back monthly, does the IRS tax the 'income'?

My father currently receives the funds from the trust, but my name is on the paperwork also.

It sounds like you are describing a loan from the trust. If that is the case, loans are neither income nor taxable. As others have said, depending on how the trust was structured, you may or may not be able to take the loan. Have an attorney review the trust and advise you on both issues.

It really depends on the wording in the original trust document, who signed it, where the money came from, and whether it's "revocable" or "irrevocable". Depending on the exact wording and where your name appears (e.g. are you named as a trustee?), it could even be illegal for you to take any money at all - so, check with an attorney and proceed carefully!

Unless the trust was tax deductible when the money was put into it (like an RRSP), I don't think that you have to pay tax on it when you take it out. Kind of like a bank account. The income that you put into a bank account was already taxed in the year that you made it so you don't have to pay tax on it when you withdraw.