You can do it through the court. A judge will have to approve it first though. No big deal really. Just google "name change ___your state___"
If you legally change your name, you'd have to amend all your documents, including your SS card, passport, licence, etc. It's going to cost you a lot of money to get all this done. Bank accounts, too.
If you don't change your name, you can use just your first name and skip middle names, but if your last name on ID contains both the grandparents' names, then that IS your last name, and shortening it for official use wouldn't be allowed.
If you legally change your name, you'd have to amend all your documents, including your SS card, passport, licence, etc. It's going to cost you a lot of money to get all this done. Bank accounts, too.