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Were you already operating and selling items with the name "Blakenship" attached thereto when you sold the medical system to them?
What if anything did the agreement state about the name "Blankenship"?
Yes. So you opened up the clinic and are proposing use or naming other products with the name after the sale. Yes, you very easily could have sold the name "Blankenship" in like or similar products.
If the products are similar and you in any way would be competiting agaist them or in a similar product line - I would be most likely to state you are infringing upon their purchased "trademark", etc.
You are really going to have to retain counsel to really look into the matter because damages in these types of situations can be extreme and the litigation very costly.
What do you call the PT clinic?
Yes, certainly you can produce a new product that does not use the Blankenship name - unless you signed a "non-compete" agreement with the purchasers. If that is so, then it's what the agreement states.
Using the name "Blankenship, Inc." is certainly not a trademark infringement in and of itself. There are many companies (thousands) who use similar names.
You do admit that your name had instant recognition then.
Is that what the Blankenship System also did - functional capacity evaluations and impairment ratings?