Although O. Henry does not tell us in “One Thousand Dollars” why Gillian wants Miss Hayden to think that his uncle willed her the money, we can have a pretty good guess as to why he does. We can surmise that he does not want her to feel grateful to him and to, therefore, feel that she has to accept his offer of his love. We can also surmise that he wants to be sure she will accept the money.
We can see in this story that Gillian must be very much in love with Miss Hayden. He tells her he loves her. He writes that she is “the best and dearest woman on earth.” At the end of the story, he gives up his chance to inherit so that the money will go to her. Clearly, he loves her.
Gillian must have enough self-respect and moral fiber that he does not want Miss Hayden to accept his love out of obligation. He would presumably like to marry her, but only if she really wants to marry him. He does not want her to marry him because she feels she ought to. If he had told her that the money was from him, she might have felt that she should be grateful to him.
Gillian may also think that Miss Hayden would not want to take charity from him. He might fear that she would be too proud to accept the money if she knew that it came from him rather than his uncle. Therefore, he says that it is from his uncle so that she will be sure to accept it.
For either of these two reasons, or for a mixture of the two, Gillian lets Miss Hayden think that the money came from his uncle.