The set of names the equipped creature has includes the names of all nonlegendary creature cards in the Oracle card reference, including the back faces of double-faced cards. Notably, the equipped creature won't gain the names of tokens, such as Zombie Token, Goblin Token, and similar. It also won't gain the names of noncreature cards that have become creatures, such as a Wandering Fumarole that has become a creature.

If you named any nonlegendary creature card for hidden agenda or draft abilities that refer to a creature on the battlefield, the equipped creature will have that name and will qualify for any relevant bonuses. For example, equipping Spy Kit to Noble Banneret will enable Noble Banneret's last ability (as long as you noted a nonlegendary card name for it).

Some creature cards have abilities that function during the draft and additional abilities that refer to cards you exiled or information you noted with "cards named [this card's name]." These abilities are linked, so equipping Spy Kit to such a creature won't affect the set of cards it exiled or the information you noted.