To get access to RD races in SGP you have to be a Premium Member in the first place. Has nothing to do with Discord.
SGP also uses you real name. You can link your Discord to that platform to join communities that require it.
But then again you dont need the real name in Discord, cause you already have it "registered" in SGP which is connected to Discord with your name. So in the races you sign up for, it will always show your real name.
If there will be any issues in the future, the admins will tell you in advance. Normally no one is getting kicked from a server without a warning and a request to change something. So far I didnt had any issues not using my real name in Discord and like 70-80% of the drivers here also only using their nick name.
Edit: Just realized. We use Discord as a replacement for Teamspeak, the real name was required there. That might be why it is asked now. But again, you have your real name here, real name in the race sign up, real name on the AC server. So the admins know who you are and if you have premium
easiest would be to use the same name in Discord as you use as your forum nick, most of us doing it that way.