There are two general categories of things you can do with it.
First, you can use it to power up cards that look for other permanents with a particular name. Biovisionary is probably the strongest example here. Here are a few more examples: Cleric of the Forward Order, Shadowborn Apostle, and Urborg Panther.
Second, you can use it to exploit cards that care about things with the "same name". This works because Conspiracy: Take the Crown added the following rule to Magic:
201.2b If an object has more than one name, it has the same name as another object if there are one or more names that both objects have in common.
The best use of this I can think of is to get Spy Kit on an opponent's non-black creature (such as via Donate or Act of Treason) and then target that creature with Eradicate, which will exile all non-legendary creatures from their hand, library, and graveyard, which is absolutely devastating to many decks. You can also use this for slightly less grand effects, such as exiling all non-legendary non-token creatures with Detention Sphere or bouncing them with Echoing Truth. If all your creatures are legendary, these can be pretty one-sided; you trade one creature (equipped with Spy Kit) for a bunch of theirs.