The only similar situation I could find is that tom-riddle is a synonym of voldemort. There is no bruce-wayne tag. I didn't make any attempt to search for other secret identities to see if any of them have tags.
Yes, they should be synonyms.
Granted, one is a secret identity and there could be questions about only him, but a fan of Superman might not search for "Clark Kent" in order to find such a question.
Although the mods can do this work, I see the day-to-day of this as community activity. As such, I have suggested clark-kent as a synonym for superman, since I had the requisite rep in superman. Those who can review synonyms can up or down vote the suggestion accordingly.
As an aside, I wouldn't create secret identity tags just to match things up, but if someone feels the need when they create new questions, then we can take care of them then.