If an ability of an object refers to that object by name, and an object with a different name gains that ability, each instance of the first name in the gained ability that refers to the first object by name should be treated as the second name.
Example: Quicksilver Elemental says, in part, “: Quicksilver Elemental gains all activated abilities of target creature until end of turn.” If it gains an ability that says “: Regenerate Cudgel Troll,” activating that ability will regenerate Quicksilver Elemental, not the Cudgel Troll it gained the ability from.