According to Dustin Griffin, writing in Englewood: Historical sketches, he tells us that it is the opinion of local historian Robert Griffin, that the name "Tryon Ave" remains a real mystery. Found as early as the 1876 maps of Englewood, at first glance it would appear to be named for William Tryon, last Royal Governor of New York... but exactly becasue of this he was a target of real resentment on the part of the revoutionaries of 1776 and thus unlikely as a candidate for the naming of a road here. So we really dont know. 
- Griffin et al, Dustin (2003). Englewood: Historical Sketches. Englewood Historical Society. p. 58.