Peer info?

Setting tags for a peer is local, right (not broadcasted)?

If I’ve already traded with someone, instead of showing their onion address first, it would be nicer if it showed easily identified account info such as their name (as used in the payee field).

Yes local.

Name is only available if you did a fiat transfer where the name is included (OKPAY not). But, yes might be added in future.