Yes, Arabs use "Ibn" and jews use "Ben". Slavs use father's name and "ich" suffix. People in Iceland use different kind of patronimics.

You can either use just one name field if your logic doesn't need a name or surname or provide two fields for name and surname and let the user handle the splitting.

I have three first names. When I fill a form, if it's an official form or if it's for business purposes I fill all my names as first name, if not, I only write the name I use.

Ibn is a patronym, but a kunya is the other way: your name is the name of your child. E.g. Palestine’s Abbas is also “Abu Mazen”, the father of Mazen.