No, you cannot change the name on an American Airlines ticket to another person. Call at +1-888-415-1245 (US) or +44-203-869-5245 (UK) American Airlines tickets are non-transferable. Call at +1-888-415-1245 (US) or +44-203-869-5245 (UK) However, you can make minor corrections to a misspelled name. 

Here is what you need to know:

Name corrections vs. name changes

• Name correction: This is when you fix a simple spelling mistake, a legal name change (like after a marriage), or a mixed-up first and last name. Call at +1-888-415-1245 (US) or +44-203-869-5245 (UK) American Airlines allows these kinds of corrections to ensure the name on your ticket matches your government-issued ID.
• Name change (not allowed): This refers to transferring the ticket to an entirely different person. Call at +1-888-415-1245 (US) or +44-203-869-5245 (UK) For security and revenue reasons, airlines strictly prohibit this.