When using one's name in a foreign language, it is common to change:
* phonetics, to be easier to parse (so that others will get the correct spelling). Interesting cross-alphabet case: most people named "Artem" introduce themselves as [artem], rather than [artjom].
* spelling, to look more standard (grey area when different alphabets are involved)
* the name altogether (many Chinese do this; sometimes one intentionally chooses a similar name e.g. "Sin-Ting" becomes "Cindy", "Ke-Min" becomes "Kevin", "Yi-Lan" becomes "Elaine")
I think people tend to be more attached to written form of their names than to the phonetics (which is often hopeless anyway!), and this makes sense especially if you want to avoid red tape.
I seem to err on the side of authenticism in phonetics, and in English I say my name almost exactly as I do in my dialect of Northeast Brazilian Portuguese: [guʃtávw], often with a slightly mumbled first syllable. This baffles some people, and leads to lots of errors: "Mustafa" and "Kristafo" seem to happen equally often (maybe 10% of the time altogether). Almost half the time, people don't hear the last vowel: "Gustav".
Anglophones who have never seen my name before often say [gʌstejvo] or [gʌstavo]. I am perfectly happy with [gustavo] (which is what most people say at first sight, and it's how São Paulo folks pronounce it), but if you are Hungarian or Schwäbisch, saying [guʃtavo] may come naturally and will put a smile on my face. If you are Romanian, [gustavu] may be natural for you. Anglophones, please don't try too hard.
(Thanks to
http://ipa.typeit.org/)