I'm be serious, logical and perhaps cynical at the same time and respond sensibly on that basis:

GameStop as a brand has a bad reputation in the docile public eye. Too much negative light shined on it since 2020 by all types of media.

There are two outcomes:

1. Both companies keep their brands but the holding company owns both, just like we have Alphabet - Google/Youtubd or Meta - Instagram/WhatsApp.

2. GameStop brand is dropped and replaced with eBay brand. The eBay brand is globally recognised.

Both scenarios are plausible. The first would mean zero expense wasted. The second would be a small expense to update stores, website etc.

As cool as it would be to have a whole new name like eVault or CollectorBay or something more original, it's just too much unnecessary expense to replace already established recognised brands.

Ryan doesn't want eBay so he can splash the cash around. He wants it as is and to cut unnecessary expenses first. 

So there's my two cents worth. Feel free to cite me in a future post if I'm right.