If I’m named as the executor or personal representative in the will can I start administering the estate?

No.  You must first file the will with the probate court, establish the will’s validity, and be formally appointed as executor or personal representative.  Before rushing off to the court house, you should be sure that you have the correct will.  Sometimes a family member will find a will, assume it’s the right one and head on down to the court house only to later discover that there is a more recent will or trust that replaced the revoked the prior will.