Is it a common thing in Europe to not name your newborn for several weeks or even months?

Not in Britain. Maybe elsewhere. Europe is quite big and comprises many different cultures. ;)

As @richardhenry said, in the UK, there’s a set period within which you legally have to register a baby’s name. I feel like it might be quite a short period, like 10 days or something.

Rest of Europe I couldn’t speak for. Remember “Europe” is not one legal entity, each country has its own distinct legal system.