What is the meaning of this 征 in this sentence please What is 征 here please? I guess it is either 征求 or 征集。Would either fit the bill? Maybe 征名 is a word？ I think it is really '征集名字‘。

The background is, 兰州的‘读者文摘’ had to change the name of their magazine, because the American '读者文摘‘ had already registered that name.

编辑部马上行动，在杂志上刊登了征名启事。征名启事刊出后，读者的来信如雪片般飞来。

The Editorial Department took swift action, they published an announcement in the magazine, calling for/soliciting (new) names for their publication.

Any chance 征 could be 征询 的‘征’？？
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.