Is the title "The Gift of the Magi" appropriate?

This would probably be a personal judgment call, as no one can dictate whether you should think the title of a story works or not. That being said, we can try to discuss this title within the context of the story to try to discern how it relates to the story itself and speculate as to why O. Henry might have chosen the title he did.
First of all, it's important to note that the magi is in reference to a story from the Bible about the wise men who bring gifts for the birth of Christ. However, at the end of the story, O. Henry invokes their example, citing the magi as the ones who "invented the art of giving Christmas presents," and he ties that example back to his main protagonists who live so many centuries removed: this is ultimately a story of sacrifice, of giving up your own precious possessions for the happiness of a loved one. Della sacrifices her hair so that she can get her husband a fob chain for his watch, and Jim sacrifices his watch for combs for his wife's hair.
To a cynic, this story would be a cruelly ironic one: each sacrifices for the other and is left with nothing. But that is not O. Henry's meaning, because for O. Henry, that act of sacrifice and devotion is far more powerful than any material possessions. In their willingness to sacrifice for one another, Della and Jim have been placed within a tradition that stretches back to the Magi themselves: they understand the true nature of gift-giving and the true value in it. Thus, O. Henry writes, "they are wisest. They are the magi."
With that being said, I would suggest that this particular title primarily works on the thematic and symbolic level rather than the literal. It's about the spirit of gift-giving, a spirit which Jim and Della embody, but this is a spirit which is, in some ways, larger than Jim and Della themselves. It inhabits the center of Christmas tradition, stretching all the way back to its earliest days.