"My name is Adam."
Translation:Nazywam się Adam.
If you mean "na" in another possible answer "Mam na imię Adam" or "Na imię mi Adam"- it is simply an idiom. Just remember, that when you say the verb "mieć" + someone's first name, you always need to add "na" before "imię". This is by far less commom with surname (some people say so, but you do not have to use "na" with a surname). So this way you may distinguish first name from surname.
If you mean "na" in the beginning of the verb "nazywać/nazywać się" (imperfective) https://sjp.pwn.pl/szukaj/nazywa%C4%87.html - it is just a part of the verb. In Polish there are plenty of verbs that share the same stem, but have different prefixes, thus changing a little bit their meaning. In this case however, in modern language there is only one other verb in the family "nazwać/nazwać się" (perfective), and no more other variants , there is only an alchaic verb without the prefix "zwać/zwać się" which means basically the same, but less formal.