It would have to be evaluated on a case-by-case basis. Gnarlie points out two viable possibilities. I'll add a third possibility in that it's personal preference due to the totality of training. As an example, I teach Kong Soo Do Karate. It's pretty much redundant on purpose. I started off in Okinawan arts and that is my root. Later on I trained Korean (as well as Israeli, Japanese, Chinese etc). In essence, a lot of training methodology went into what I/we teach. I chose a Korean name for the art to honor my longest association with my instructor who is a Korean arts master. But, and this isn't meant in any disrespectful manner, I don't use Korean terminology at all. I prefer Okinawan terminology as it was the first I learned and those arts still have a profound impact on what I now teach. So as with the arts name, I honor all of my training and former instructors in some way, shape or form by what and how we teach.
Secondly, though rare, I have seen Korean masters still use Okinawan terminology and call themselves Sensei. Perhaps this is to honor the roots from which their art came? Perhaps personal preference?
As with anything, names and terminology are secondary to good teaching. If the teaching is sound then that is the primary goal. I've often joked that I could call my art 'Dave's Bait, Tackle and Kung Fu Emporium'. As long as my students find value in what I offer the name doesn't matter.