The ship's funnel (chimney) did have the initials "White Star Line" written on it, which could be mistaken for "Liverpool" by someone unfamiliar with the ship's markings.
However, "White Star Line" was the name of the shipping company that owned the Titanic, not the city of Liverpool.
The Titanic was built in Belfast, Ireland, and its home port was Southampton, England. Liverpool was a major port for transatlantic liners, but it was not directly associated with the Titanic.