I am currently trying to add my ITA Volare Premium Skyteam Elite Plus membership number to my KLM reward booking. It is not possible and also customer support could not add it.

I suspect the problem could be that my first name in ITA Volare includes my middle name as well, but in KLM ticket and account I only have my first name.
Could this name mismatch also lead to trouble getting my status recognized while trying to enter the lounge in Paris and Amsterdam?