You can customize your wallet address, yes.
The custodial wallet #WalletOfSatoshi and the non-custodial #Zeus give you the ability to change your address. Its a service they provide after you send/receive a certain amouny of satoshi (100000 sats i think)

Other wallets offer this kind of service, but i never checked yet (maybe even #Breeze)

https://www.walletofsatoshi.com/

https://zeusln.com/