Provided that is all a WIP, it's a minor choice that shouldn't have great consequences like the other nameless choices.
Personally, I've chosen the cockring, since the bracelet has the worst stat and I have th neck slot occupied with the amulet of strong mind.
I think you're supposed to choose the bracelet if you want to attack him, the collar if you want to defend from him and the cockring if you want to fuck him.
I don't know if some effects of the bracelet or the collar are already implemented, but if you have sex with him while wearing the cockring, Nameless comments something positive about you, like that he's glad you're wearing his gift. My hypotesis is that Nameless has an hidden like sistem and having sex wearing the cockring rewards you more likes than having sex without it.
On that note I'm not suggesting to have sex with Nameless, but if you're having sex with him I think is better to equip his cockring (I don't know if wearing his others gifts does something in any occasion).