Use my Gamertag from Xbox when playing on PC

Hi, I have an apex legends question. Mainly related to using accounts cross platform.

I am aware that cross progression on Apex does not work so I can not get my items or progression from one platform to another. However my question is specifically about my EA ID which shows as my display name in game.

When I play on the Xbox, my display name is my Gamertag and this is what people see when I play with them. I have set up an ea account on my pc and linked it with my xbox live account. If I try to use the display name for Apex on pc so it's the same as my Gamertag it says that it's already been taken. I'm just confused if it's saying this because this is used for my xbox account?

Does anyone know if I can use the same display name on my pc as i do on the Xbox (Gamertag) and when it shows as taken is this because my xbox uses that name or does xbox have a separate name pool or uses my Gamertag as an alias and it's actually been taken by another user who registered elsewhere?