My DH changed his name - had an unpronounceable and unspellable Eastern European name, he’s a naturalized citizen - and we discovered there are two methods (or were in the early 90s), one with a court thing (sorry I’m dumb about the correct terminology) and one just notifying the local newspaper a certain number of times. We did it the second way because it was cheaper.
I am not sure I understand. Your DH(BTW, what is a DH?, sorry to ask).
Your DH is going by an alias and you used only the newspaper to announce but, it is not a legal name. It is an easier name to pronounce and posting to the newspaper cost only a couple of bucks?
The route of changing your name and identity by legal means is expensive and time consuming you are required to post your new status in a newspaper anyway. This is not a good analogy but think of even a sex change operation. Your current is Michael but due to your sex change you need to create a new identity and you want to be Marcia. You can do that and your documents and entities with an interest in your identity will be consistent under the law.
If your DH did not “legally” change their identity, then they are AKA.
AKA costs less and nothing wrong with it, at all.