Your descriptions of how you pronounce your names are a bit confusing. Your first names are well-known in Ukraine. I’m thinking about the Americans Michael Jackson and the actor and singer Jared Leto. In Ukrainian Cyrillic letters Джаред (Jared) and Майкл (Michael) pronounced in the way those singers do themselves and according to your first alternatives.
Your last name Chomyc is more complicated. Do you mean you pronounce the initial sound as CH in chicken? Then it should be written Ч in Ukrainian as well as in Russian. But when I see here that you pronounce
myc as Mic or Mack I realize that the transliterations I gave you in the Russian thread do not fit. For your pronunciation of Chomyc as cho-mik the Ukrainian Cyrillic letters make it Чомик (but as Mick Jagger's first name is written Мік it might be possible to write Чомік). In Russian it would be Чомик. With the Mack- alternative you should write Чомак in both languages. If I were you I would choose Чомак. When I ua-googled for last names on Ukrainian sites I didn’t find Чомік but I found Чомак. A Turkish professor was named Чомак for example. On a Ukrainian forum I read that family names that end with ик have changed the ordinary й- ending into ик.
«ÔÐÀÇÀ» - ôîðóì
In short, your names in Ukrainian are Джаред Майкл Чомак (or Чомик / Чомік).