The Woolwich bit is where they were based. Arsenal refers to the munitions works. So they are now named after a type of factory, not a place.
But when they were formed they were named after an area – ie. Woolwich, and only dropped the Woolwich when they left that area.
Port Vale on the other hand, were named after a section of the canal that had not been known as Port Vale for many years when the club was formed.
Techically, both clubs were once named after an area that either once existed, or where they were once located.
Best Regards
P. Edant