There is the diceware method to make passwords random and strong to crack. But is it advisable to use this method to make random names for email addresses? That is the concern I have, when a person makes a random email address, they inevitably introduce things with which they can be identified, breaking the previously stated randomness, what ways are there to avoid this?
That is a good idea just so that you don't have to think about any potential privacy issues. Your email could be {firstword}{secondword}{4 numbers} and so long as the words and numbers are randomly generated, you can avoid accidentally including personal references or biases.
Your username does not need to be high-entropy, though. It will be semi-public. So it's not about strength against dictionary attack or similar, it is just about leaving the selection process up to a random process that isn't witnessed by a third party. You can write scripts that will generate these kinds of things using Python and the faker library.
like why do you need email addresses? use temp mail for garbage registrations and two-three stationary emails which you remember for stuff which is linked anyway
I usually pick usernames and email addresses with diceware. Unless I've got a zinger in mind like with the propter hog one.