Probably „nazywam się” because it should be followed by forename and surname. The second popular choice would be „Jestem x” - s convenient way of giving only your forename (but if you want you can also add your surname).
When you shake hands with someone unknown you would probably go with: „Cześć, Paweł (jestem)”. Jestem is not needed.
I am called Adam? It seems like a more literal translation to help me remember the meaning of... nazywać. Correct that if I am wrong, please.
The most literal is "I call myself Adam", but that is just too weird in English. And although it's the most literal translation, it changes the real meaning.
"I am called" works.
Just out of interest, would the perfective form "nazwać" only be used for the actual singular event of naming, say at a christening, or the moment of choosing a name?
Not sure about the christening (it's not the priest's decision after all), but for sure when choosing the name. Well, generally "nazwać" as a perfective verb cannot be used in the Present Tense, so you always refer either to the past or the future.
"Nazwaliśmy syna Adam" = We named our son Adam.
Brilliant. Thanks again, Jellei. Think I've got the hang of it now. (Well, of this part anyway...)
Why is "my name's Adam" wrong? It is just the short version of "my name is Adam". I think it should be accepted too.
Normally contractions are accepted automatically, so I am surprised that not here. Added now.
To me this is not a standard contraction, like "can't", "it's"... You wouldn't find it in any English textbooks, since it is just too casual. Imo, there is no need to include it in every answer.
Poprawnie w języku polskim "mam na imię Adam". Nazywam się Kowalski, Wiśniewski etc.