There are many abilities that reference the name of the card which has the ability, either with the full name or part thereof. For example, and both refer to their own name with their ability.
When another card gains such an ability, the text should be read as referencing the new card's name. For instance, if both and are in play, Vivien can tap to search for another card named "Vivien the Enchantress." If banishes and gains the abilities of , he will look to see if another card named "Grigori Rasputin" has been summoned when creating a copy.
In effect, when reading an ability which references the name of the card on which it is printed, you replace the name with a grammatically appropriate version of "this card."