Of course the solution depends what kind of reporting request you have. If only the assignment group names are relevant, then only a single new field is needed and you concatenate the ticket's assignment groups after each other.
Remember that if ticket is reassigned multiple times, just having a calculation in a last post won't work: if the ticket is assigned to three teams during it's lifetime, one assignment grouop value will be left out.
Again, depending on your reporting tools the ultimate solution is to look a table [yourSMdatabase].[dbo].[PROBLEM1M1]. (My syntax is derived from MSSQL database world, it's different if Oracle is used.) That table holds IM ticket versions from it's opening until it's closed. If possible, make a SQL search to that table and retrieve the assignment group names which are different.