HIDE My EMAIL,Is it possible to create your own “hide my email” user name? First, I did not know that ICloud would generate this new feature without my permission. Some of the new user names seem to be on a personal level. Thank you

Hide My Email automatically creates a random email address for websites you use it with. You do not need to use Hide my Email if you do not want to. Hide My Email only works if you have the option turned on in Settings and you select the Hide My email option when creating an account on a website

You can manually create addresses if you want to. In Settings you can generate Hide My Email addresses, they are random and unique.

It has absolutely nothing to do with any conversations you had, its a random unique address. Mostly just a jumble of letters. If somehow it matches with something you said in a conversation, its merely a coincidence. You can generate a different address by tapping on "Get New Address", and it will generate a new one.

click here ➜ Set up and use Hide My Email in iCloud+ on all your devices - Apple Support

Also, you need to be paying for iCloud Storage to have access to the option.

Where exactly are you seeing these addresses that use part of your conversations?