The name's [ʔn̩]. [ˈzo̞.ʔn̩]

How do I pronounce Zotn, why does it matter and where does it come from anyway?

Let us begin with the second question: it does not.
And you can clearly see the answer to the first question in the title.

So with those out of the way, you may wonder why I chose these four letters to represent my attention-seeking artistic side? 'Tis simple: Zolee, Zoley, and other variations of my name is already in use with the exception of Zoleigh, which is longer and harder to spell (especially for non-native English speakers).

Only one question remains now: why this pronunciation? How does [ˈzoltaːn] becomes [ˈzo̞.ʔn̩]? Well, it's from my approximation of Zoltán's English pronunciation. Here's the breakdown:

• In Hungarian, the stress is always on the first syllable, but in this name, the long vowel is on the unstressed syllable; this doesn't make it short, although in my region and during fast speaking, long vowels tend to shorten (in addition that a /ɒ/ and á /aː/ are two different sounds), while in English, stressed vowels tend to lengthen. Add all of these together, the /aː/ reduces to a schwa-like unstressed central vowel.
• Schwa + n can easily (and often do) become a syllabic n /n̩/ in English
• The o is marked to be a mid vowel, because that was originally an /o/ sound, but in English, it would probably be an /ɔ/ instead. Even my pronunciation may vary, so /o̞/ is used as a compromise.
• The z is just a /z/, no changes there.
• In my dialect of Hungarian and especially in my own speech, syllable-final ls tend to disappear and lengthen preceding vowel -- similar thing happens in multiple English (language) dialects, so it's done here as well.
• Finally, the t-glottalization is done, because it fits; the t is followed by a (syllabic) n, which is the perfect place for a t to become a glottal stop.

QED

tl;dr Zoltán > Zoltən > Zotən > Zotn