I guess it is always subjective. If you have no concerns how you are identified outside the organization you belong to (even if it is an organization of one) then don't sweat it.
Practice as well as you can and take away what you can....and if this is sufficient to you, at least in the interim, who cares about a name. A rose by any other name smells as sweet.
And I will give kudos to your instructor for not reinventing the wheel. He gave his nod to the standup portion in the style's name, if nothing else. Better than calling it James-ryu, or Smith-kan Karate.