What is the meaning of this 征 in this sentence please
Your guess is right. It means 征求 or 征集。In English, it means "Call for", and here it is "call for names". The dictionary definitions are close.

For 征询, 征询 = 征求、询问. However, it is usually used to ask for opinions. The word 征 in 征询 is indeed the same though.