There are some cases where it is sensible to conflate a group name with its members; but IMO some distinction needs to be possible.
For instance: notification emails and the "My Tickets" screen make no distinction at all; "...assigned to you..." is the phrase, and it's the same whether it's assigned to me or to my group.
A ticket assigned to "IT Service Desk" is NOT assigned to "Me". It's essentially unassigned within a group.
This distinction is very important when you're actually managing your workload.
Let's have a separate notification, mutually exclusive from "...assigned to you" which says "...assigned to your group {{group name}}".