Making your Old Nicknames private for 3rd Party Sites

Sites like NameMC makes that information public and it can't be hidden because they gather it directly from the Minecraft accounts, it would be so nice to have an option in Minecraft.net website to make that information private, for example let's say I have my real name in my account years ago, and now I decide to make content for internet, now I have to hidde my current nickname in the game because people can easily find my identity just searching my nickname in that site.

I think privacity is something that should be respected, this is just an example but I think there's a bunch of people that would prefeer having that option.

Thanks for reading