I think renaming the client to Bitcoin Wallet
is very good idea
During an interview, I used the term "Bitcoin Client" and had to go on a tangent about what a "client" was. If I had said "Bitcoin Wallet" it would have instantly clicked. I don't think people are interested in a technical lesson on what a client is.
What does it do? It's where you store (and to a lesser extent manage) your money. It's a wallet.
no because i expect the client to be able to handle multiple wallets. for example a "load" function which pops up a file-search-dialog followed by a password prompt (or maybe usb dongle or stuff).
Technically, yes, you are correct. (load function search dialogue password prompt usb dongle.
I would definitely prefer to call the client a "bitcoin wallet", and say "technically, it stores multiple wallets". I would also prefer to call the actual wallet.dat a "bitcoin wallet file", or "bitcoin wallet.dat file", instead of the misleading bitcoin wallet.