General:
* Accompany
* Attend
* Guide
* Convoy
* See off
* Protect
* Shepherd
Formal:
* Attend
* Chaperone
* Companion
* Protegé
* Escour (archaic)
Informal:
* Walk someone out
* See someone home
* Look after
* Tag along
* Shadow
Specific to Security:
* Guard
* Bodyguard
* Protection detail
* Security personnel
Other:
* Go with
* Travel with
* Take someone somewhere
Please note: The best synonym depends on the specific context of your sentence.