Yes, but typically the loan "originator" remains responsible unless the actual loan is transfered to the new purchaser.
Letting someone "take over payments" on your loan is a very bad idea. If there...
You and the person wanting to take over the payments, go in a sit down with the lender who holds the note, and talk about it. The lender must agree to this for it to happen.
IF your credit is good enough to qualify for the loan, you and the other person will meet with the LENDER and do the paperwork. Not much different from getting your own loan. Main advantage is you...