But you can still have the two accounts related as FulI suggested if that's what he wants to do. This is pretty much the scenario you & I were discussing in last night's PMs, except I am not interested in becoming a delegate, at least not now.
But FulI's question is still unanswered. If the current, registered delegate account is delg, creating and registering a new account named nodelg.delg would make the current delg account the "root". That is actually backwards from what FulI asked for, which is to make the delg account the subaccount, like delg.newName. That I don't know how to do or if that's even possible.
If it is, then riverhead can explain how to do it and if desired have the two accounts (however they're related) live in separate wallets. That's what our PM was about.