In today's Europe, when we hear a name, we usually don't associate it with a given meaning - it's just a name of a person. However, it's not like that everywhere in the world - even in Japan and China, we can still see names being chosen for their meaning.
Now, this is not to say we never associate names with meanings - just that most people do not do it most of the time. But we did use to - be it Marcus or Kar(i)l, names did have clear meanings.
But when did this end? Was it around the advent of widespread Christianity, when Hebrew- and Greek-origin names displaced etymologically transparent native names? Was it during the Lutheran era or secularisation of Europe, when names stopped being associated with their respective Saints? Or is it a process that was individual to each name as they were borrowed to another language where they had no inherent significance, and can't be generalised into a trend?
EDIT In this post, I mean "first names" or "given names" when talking about names.
EDIT 2 Edited out an accidental word
I’m no expert but, as far as I’m aware, a lot of it has to do with the origin of European names, especially English names. So most European names are Christian names, and generally derive from the bible. Lots of these names had meanings in ancient Hebrew but these didn’t pass on when they were borrowed by new languages. For example, my name is John, but this originally comes from the Hebrew word, Yohanan, meaning “favoured by God”. https://en.m.wiktionary.org/wiki/John This mutated through Latin, early French, Middle English to become the modern name of John and therefore, for the average English speaker, picking a biblical, or even traditional name, is far removed from the original Hebrew meaning, of which they’re probably completely unaware. This isn’t, however, the case for all European names. I also speak Russian and Russians use many Slavic names, for example, Vladimir, Svetlana, Bogdan etc. which are derived not from Hebrew or biblical names, but from Slavic language roots. As such, Russians are aware that Vladimir means “the peaceful ruler” or something similar, in old Slavic. Similarly to English, most Russians don’t actually know the etymology or original meaning of Ivan, the Slavic form of John, only that it’s a biblical/ traditional name.