It is a double entendre, that is, it has a double meaning.
By stating the phrase "Soldier's Home", Hemingway is saying that:
a) He will be talking about the home of the soldier.
b) He will be talking about the fact that the soldier is back.
The story talks about both things: The soldier is home, and we get to see the dynamics of the household once he gets there.
We know that, in the story, the soldier IS at his house but he is not "at home" as nobody understands the situation from which he has just surfaced from. Everyone evades him, and they refuse to understand him.
Hence, it is an ironic title to call it that way because the soldier is neither at home nor does he really have a home where he can feel at ease to understand his circumstances. One more instance of Hemingway's genius!
Though Hemingway’s sentences are brief, they are not necessarily uncomplicated. In paragraph 15, for example, one might notice that the following basically simple sentence contains two adjective clauses ("they were in," "he was in"), and it therefore is complex even though short: "But the world they were in was not the world he was in." The last sentence in paragraph 5, involving the "who" constructions, is as complex as any to be found anywhere. Once the section of the story involving dialogue commences (paragraph 17), the words are short and specific, in keeping with the tensions within the family and also in keeping with the general inarticulateness of the speakers.