ENotes provides an excellent analysis of why the character is named Phoenix.
The phoenix is a bird from Indian and other ancient cultures' mythology, a sacred firebird that rises from its own ashes after death by burning.
For you to consider as you analyze:
- How is the character of Phoenix sacred? How is she an image of an admirable, ethical, worthy-to-be-esteemed woman?
- How has she been "burned" by life's circumstance?
- How does she "rise again" despite her difficulty?
For evidence of her suffering, begin with the situation of her grandson and his injured throat. Note how she is found (struggling in a ditch) and needing rescue. Note how she is treated due to racism, especially in the name she is called -- "Granny" and in the taunting with the gun. And then explain in your analysis how she overcomes all these obstacles through both words and deeds.
Finally, consider the title of the story, "A Worn Path." Is the title only referencing the path, or taking into the account the fact that this woman's life is worn down with struggle, just as fire reduces something to ash? And yet, the path remains...
Any time you see a name that sounds familiar of a character, it is worth researching for its various connotations.