@PeterJones said:
[IANAL, and I don’t know the legal term for a non-registered trademark]
An unregistered trademark, sometimes informally called a common law trademark, is an enforceable mark created by a business or individual to signify or distinguish a product or service.
–For future reference.
The stronger case needs to be made as you mention to differentiate what could be called a trademark name versus a generically descriptive name. Such as the difference between Borax as a chemical and Borax as a trademarked product name. I am not a lawyer [IANAL], either, but I have done legal research from time to time, on these types of subjects as well, in the past.