Can my fellow passengers simply join me on the day ticket for Germany?

Yes. You can use your regional day ticket or day ticket for Germany as a low-cost group ticket. Your fellow passengers can join you on the way.

However, the number and identities of the people who travel with you are already determined when you purchase the ticket. You therefore cannot change your travel companions subsequently.
Passengers entered on the ticket must show a valid ID document during ticket inspection to verify their identity.