From The HSK acadamy site, it seems that 叫 can be used in two contexts.
First, it can be used to say someone called someone else:
There is no translation given, but I think it means mum and dad call me.
In the second and third examples on this page,
I think 叫 is here used for giving or asking someones name. I would translate the second sentence as My name is 李明, and the third as Lady, what is your name? However, this is always used together with 名字, which means name. However, I've also seen simply
- 我叫 Wythagoras
for simply my name is Wythagoras (not my real name, by the way).
I am a bit confused by all the different usages of 叫, so the question is: In what context can 叫 be used for saying that someone is calling someone (as in the first sentence) and when for asking a name, when should 名字 be used with 叫 and when can it be left out?