(Going on the two I know) - Imogen and Tamsin have arty, academic parents. They're both good at crafts, and both quite girly in a non-pink-princess way. They do well at school and university, not outstandingly brilliant at anything, but good all-rounders, and they're popular, without being the life and soul of the party.
I've never thought of Imogen as a 'posh' name at all. I don't know anyone with this name nor heard of anyone irl with this name except unfortunately Imogen Thomas. I have always thought it wasn't popular but that may be due to having a harsh sound with the 'uh' in the middle.
It's great to hear other people's opinions as it gives a different and sometimes eye opening perspective .