How is the the title "This Is What It Means to Say Phoenix, Arizona" significant to the story?
In addition to the symbolism of the phoenix mentioned above, I would add the importance of the title's suggestion that the meaning of "Phoenix, Arizona" is different than what one might assume.
We see this same idea with both Victor and Thomas, both in relation to each other and toward the other familial relationships in each of their lives. The perceptions and impressions each of these characters holds about each other and other individuals in their lives proves to be incomplete and in many ways inaccurate. Through their conversation during their journey to and from Arizona, Victor and Thomas have a chance to explore those misconceptions, and although they are not able to fully repair their relationships, we sense they are beginning to see their world from one another's perspective. We sense that the "meaning" of such things that have been taken for granted are finally beginning to change.
The meaning of Sherman Alexie's “This Is What It Means to Say Phoenix, Arizona” is amplified by the story's symbolism. The story's title, among other elements in this story, is significant. Phoenix is not only a city in Arizona but also the name of a bird in Egyptian mythology that rises from its own ashes and is reborn, making it a symbol of immortality and regeneration. Victor and Thomas Builds-the-Fire travel to Phoenix and, in the hot Arizona summer, step inside Victor's father's trailer to reclaim, literally and figuratively, that which has been lost. It is not only Victor's father's ashes, but also the ashes of Victor's own life, which Victor seems ready to grasp by this story's end. Thomas Builds-the-Fire is the character and agent, as his name literally indicates, who has built the fire under Victor.
Think of how a phoenix can be reborn. The story is about a sort of rebirth for Victor where he finds himself, thanks to Thomas-Builds-the-Fire. Victor comes to peace with himself, where before he was very angry. His self-discovery is similar to the rebirth of a phoenix (the bird).