I'm wanting to set up a charity and want to use a public wallet for accepting donations with on Etherscan where I can have a displayed name next to the wallet like this:
How Can I Add My Name Next To Address On Etherscan?
Etherscan adds them on a case-by-case (manual) basis for now. You can add a comment to the address and then contact them asking for it to be added. However, I'm not sure if there is some sort of "importance" threshold you must meet.
The initial names that were added were things like Poloneix and Kraken, as it helped users immensely to be able to see that they were sending or receiving from an exchange rather than to a random person.
I would also like to remind people that it's not the best idea to put your name or identity on your address. Ask yourself what having your name truly adds anything to a random user's life. If the answer is "not much" then just don't do it. It is just helping you stand out from the sea of addresses so you can get an ego boost (?) and, if the account has a significant amount it in, could prompt attackers to target you.