You can choose a creature card name you've already chosen. Not getting all the style points you could, but it's allowed.

You can choose the name of any creature card that matches the condition. It does not have to be a legal card in the format you're playing or a part of your Draft or Sealed pool.

An identical mana cost includes color. For example, if Killer Cosplay becomes attached to a creature with mana cost , you couldn't name a creature card with mana cost or .

An Equipment can't become attached to a creature if it's already attached to it. That is, you can activate the equip ability targeting the creature Killer Cosplay's already attached to, but that ability resolving won't do anything. Killer Cosplay's triggered ability won't trigger.

In most cases, the equipped creature will gain all the usual copiable values of the creature card with the chosen name—that is, it will have its name, types, abilities, power, and toughness. However, if you can produce the actual card you've named, the equipped creature will also have that card's art, watermarks, and flavor text.