As long as he is on your nation page and clicks the make donation page (on your nation page) then it'll be done for you. Once he pays the name change amount, they contact you within 24 hours (as stated there) and you will get to message what you want your name changed too.
So yes someone else can pay for you, they just have to make the donation payment by clicking on your nation and then finding the "Make Donation" button. I hope that answers your question. If I made it confusing let me know and I'll try to simplify it. (Basically however you do donations with bonuses is pretty much the same way for names I believe). I've never done it myself so I can't fully verify but from the overview when I try and do a donation for someone else it seems to hold true.