For physical caches, as long as it's clearly indicated what group name cachers have used, I'm fine with it. I don't have any high terrain caches anymore, so it's not a question of one person climbing a tree to sign for a group. If I did, I would feel differently for that cache.
For earthcaches, the whole point is to teach (and learn) an earth science lesson. If a group stops by and only one person submits answers, I have to wonder how much learning went on, but I still allow it.
I typically don't cache with more than one or two other cachers, so I don't bother signing logs with a group name. Our usual caching buddies BWB3 have a 4-character name too, so it's easy to squeeze us on the log.