Hi! You may consider improving the tagging here even further by moving the Navajo name to its own tag. Please see https://wiki.openstreetmap.org/wiki/Multilingual_names. Fortunately when we move to vector maps on osm.org soon, we'll be able to set the preferred language for all features! That'll be cool.

Anyway, in this case, I believe that would mean the following additional tag:
name:nv=Tse’Bii’Ndzisgaii

Let me know if you have any questions, and thanks for your contributions!