Like a lot of UXers, you seem to think that UX doesn’t define what you design, but how to design. However, those outside our field don’t see it that way. Do a search for jobs for “UX Designer” and you’ll see that business equates “UX designer” with software user interface designer. They even slash them together: “UX/UI Designer.”
So dropping “UX” would probably lead to confusion on what you design. If you work for a software firm, are you a software designer? If you work for an insurance company, are you an actuary? Or maybe you’re the guy who arranged the cubicle farm and put that ugly sculpture in the foyer?
I don’t think UX maturity enters into it. In a Step 7 or 8 software company, the UX designers may lead, but you still need to distinguish UX designers (skilled at frontend design) from software designers (skilled at backend design). Saying, “but we’re all responsible for UX at Step 8,” doesn’t change that. To everyone in the company, the person laying out the web pages is the “UX designer,” and no one else is. She or he just has more power at Step 7/8. As an analogy, a company might say, “IT security is everyone’s responsibility,” but they’ll still need to distinguish the information security professionals, from the CISO down, from everyone else.
If you’re in a true Step 8 non-software company (say, an insurance company), where you’re responsible for customer interactions beyond the software, then you need to drop “UX,” not because it’s superfluous, but because otherwise everyone will think you’re only the web site designer. But you still can’t go with just “designer.” Rather, you’d need to replace UX with something else. I’m not sure what. Service designer?
I suspect there aren’t any individuals each responsible for all customer touchpoints. Instead, there are specialists for each touchpoint, each with their own title. Maybe at Step 8 (if it exists) everyone is devoted to customer service, and everyone relies on observation data, but each still has unique knowledge and skills, so each “designer” still needs a qualifier.