Renaming of a filegroup is SQL server can be done as below
ALTER DATABASE MyDb
MODIFY FILEGROUP Secondary NAME=MyGroup1
SELECT name FROM sys.filegroups
Important thing to note here is, we can not rename the Primary filegroup as
the name of the primary filegroup cannot be changed.
Rename means move to another group
You cannot move a database file from one filegroup to another filegroup.
instead you can create a new file on the filegroup you want to move the filegroup too and drop/recreate the objects on that filegroup