“Should a liberal gun control activist have a Navy warship named after her?”
Absolutely not! Recently, they named a USN ship after Harvey Milk and Medger Evers. Navy ships should be named after truly American heroes such as congressional medal of honor winners, or distinguished admirals or generals, or great American presidents which are few and far between (the last one being Reagan).
I would go as far to say, they should be named after places, not people. You are always going to rub some people the wrong way with naming after a person, because no matter who you are, that person will not be universally liked.
Neither of those ships are USN. They belong to the Military Sea Lift Command. hence the abbreviation USNS in front of their names. These ships are manned by civilian civil service crews. The captain has an unrestricted Masters license from the Coast Guard. They carry and transfer cargos of POL and supplies to the Naval forces at sea. They have a 10-15 man navy communications detachment on board when operating with naval units. Neither of these ships are armed.