This question is directed towards native and fluent Japanese speakers, but I would love input from anyone!

When a foreign person (in my case, American) introduces themselves to a Japanese speaker, does it matter if the person gives surname first, then given name? I prefer my surname first in Japanese and would probably like to go by "Bujeaud San", the way that natives do. But is it unusual or unnatural for a foreigner to do so? Is it more polite / natural for me to go by my given name the way I do in English at home? 

I believe it is more polite to introduce yourself with your Surname first. Such as 私はスミス・ジョンです。Hope this helps :)