Presumably you are talking about a ticket that has not yet been issued.

If it has been issued already, one cannot just give it away and change the name. Under the Terms and Conditions of most frequent flyer programs (which is where you will find the authoritative answer as to your particular carrier) you would have to return the ticket and redeposit the miles --perhaps with a fee -- and then get a new ticket issued in the passenger's name.

In the early 1980s, many programs allowed tickets to be issued only to passengers with the same surname. With more women keeping their maiden names even after marriage, and a demand by frequent flyers to be able to actually use the awards -- after all, we want our own families to get status, too! -- the airlines liberalized their policies.

But not all carriers allow gifting tickets to whomever one pleases. Qantas still require that there be a close family relationship. There may be others. Check your T & C.