Looking to re-brand our 11 year old (long & geo specific) physical therapy practice name to one that is shorter, easier to pronounce and less geo specific. Thought is to make it more brandable as well as expandable to other areas besides improving the exit value in future. Current name is similar to 'Dayton Physical Therapy Associates' (actual city name replaced with Dayton) and it appears on top of local area search results organically. Is re-naming worth the effort in this case for the good reasons stated above?
Professionally, I mainly work with domains and brand names. And I'd advise 2 things:
(1) Whichever domain you're using to rank #1 organically for the desired search vertical, leave it alone. Building a practice on a geographically specific domain that also defines your profession is something I often recommend, boring though it may seem; and since the site is performing well (i.e. ain't broke) don't fix it.
(2) Rebranding may still be a good option for you; and since your instincts incline you to consider it, then you're probably right for the reasons you yourself outlined. When you choose a new name, then I'd recommend creating a separate site for it online. Eve if it's just a simple, inexpensive page, you can expand it later. That way you'll be transitioning with zero risk of upsetting your existing site's #1 position; and you'd be adding an additional asset to your business.
Now let's talk about that new name!