My MsSql database is being moved to a new server with a new name.

Do I just need to change the database name in the connection parameters?

Or do all of my synonyms need to be updated? I hope not as there over over 1000 of them that connect to the MsSql server.

Yes, that would be one way if you are sure that the structures did not change.

Also, make sure you change the machine's ODBC connection to point to the right place.