Jakubek Perski and other Polish Names

Hi! I'm a writer, and I'm currently authoring a short story about a Polish Jew during the WW2 era. I have a number of questions.

How does the name Jakubek Perski sound? Is Jakubek only the diminutive form of Jakub, or can my character introduce himself as such ("Perski Jakubek" would be proper in that era, correct)? CAN a person introduce themselves in the diminutive, rather than their proper name? Any suggestions for other names would be welcome, but please remember that they must be 1) from the Old Testament and 2) a popular or at least a not uncommon name for teens to early twenties in 1940 (as in, named in the 1920s).

Any and all information on the happenings in Poland during WW2 would be much appreciated. I'm well versed, but unfortunately, my vantage point from this era on the other side of the pond is most certainly lacking.

Thank you in advance!

Jakub is more proper. Jakubek is often referred to a small child.

Jakubek would be Jim as opposed to Jakub (James). Friends might call him that, although Kuba would probably be more likely. Perski is a very typically Polish Jewish name. Nationality and regional or municipal names were frequently used in the Jewish community including: Duński, Egipski, Szwed, Syryjczyk, Mazoweicki, Litwin, Poznański, Lubelski, Krakowski, Warszawski, etc.