I financed a car, then my friend took over the payment. We went to the bank to transfer the car over to her, but I still had to be on the loan as a co-signer. Last year she was still paying on the car, but the title is in just her name. How can I take my name off of the loan?
In effect to get someone off the loan they would have to refinance the loan as the sole person on the loan, which once again depends on their credit. In other words, if their creditworthiness remains bad they would need another co-signer, otherwise they can't refinance and the situation remains the same. Sometimes the institution holding the loan would allow someone to assume the loan, but this depends on (1) whether the institution will allow this and (2) the persons creditworthiness, again.
The bottom line is this was not a good call to make. Don't be an agreeable person just because someone you're friends with is in a tight spot. The only person financially responsible for you in the end is you, so you don't want to make yourself liable for someone who can't afford to finance a car on their own. It's a potentially kind, even positive gesture if your friend does the right thing, but all things held equal these sorts of transactions are often a mistake, and people pay for it down the line.
If you were allowed to "simply" take your name off of a loan because you didn't want to be on the hook in case your friend failed their payments then that would mean that the bank would have to immediately repossess the asset tied to the loan since your friend's credit is not good enough.
They only approved the loan because you provided in writing:
I am 100% liable for re-payment of this loan. Please seek me out in the event that you are not getting your money.
So since they would no longer have legal route in theory then they cannot trust your friend today the same way that they didn't trust them previously.
You can't just "take your name off the loan". The reason why banks require a co-signer is because the person applying for the loan doesn't have good enough credit, i.e. the bank is afraid that they won't keep up the payments. If you could just take your name off the loan, then the whole point of having a co-signer, from the banks point of view, would evaporate: You could co-sign so your friend or relative can get the loan, then a year later -- or a day later -- take your name off and the bank is vulnerable to the primary signer not being able and willing to pay.
If your friend is now able to qualify for a loan on her own, she could refinance under just her own name. Besides that, I don't know any way out of this for you. I'm sorry, I wish I had some easy answer, "just file form X-27B and you're free of this obligation", but I don't think there is any answer like that.
By helping your friend get the loan you have put yourself in a situation described here: you're still responsible for paying off the loan if your friend defaults, but you cannot get the car from her in case she stops paying. Actually, your situation is even worse since you're not even on the title after transferring the car to your friend, but that doesn't really matter.
Not much to do now other than to hope that your friend will be able to pay the car off without getting any money out of your pocket.