Emily is seen as a spinster in this story - an unmarried woman who is probably never going to get married. She does have an affair with one man that the town knows about. This is the affair with Homer.
The title of the story relates to the idea that Emily had no love life, as Homer is seen to disappear, leaving the romance un-concluded, as it were. However, in the end, the town discovers that Emily had indeed found (or taken) a consort in the form of a dead body.
Though this is a rather morbid notion, Emily does prove to have achieved a life of some romance, thus the title suggests that Emily does have a "rose" or has love in her life.
Another element here is the burial. Emily is being remembered and buried at the opening of the story. In this way, the rose is for Emily's grave as well as being symbolic of her (deranged) love.