The story is entitled The Ambitious Guest, because the main theme of the work is ambition.
"The title of the story focuses on the disturbing element: ambition. The guest's ambition is equated with his solitariness, his wandering, and his separation from the community of feeling enjoyed by the family."
The very idea that the stranger was out wandering in the most difficult weather conditions, creates a contrast with the family who is nestled in their cottage. The irony of the story is that both the family and the guest end up with the same fate.
"The guest himself is portrayed as having “a high and abstracted ambition.” A solitary wanderer, his dreams of making his mark are just that—dreams, reveries removed from the concreteness of domestic life as it is evoked at the beginning of the story."