You can have either they place their fingers on their noses, choosing to use the plural throughout, or the singular, their finger on their nose, which says that no matter how many player their are, each uses only one finger and has only one nose.

If you keep the singular finger and use the plural noses, you'll be picturing a very funny looking human being indeed. (Cue Davkett for a photo.)

I would set off the name with commas as an appositive, but it may not be necessary. But certainly you can have a name following a title or a descriptor like that.

...including my sister, Mary Harper.  ... including the company treasurer, Andy Reid.

You can also rewrite it: ... including John Smith, the comany president.