Thinking about it a little more, they could have gone with 力車, the actual word for rickshaw that is pronounced "riki-sha." 車屋 may have one possible translation that means rickshaw owner or business, but it's pronounced "kuruma-ya"
Always a good idea to ask someone before picking your name out of the dictionary. That's why when I made hanko-square.com I encouraged my client to offer the consultation service option for all hanko orders in case people want their name in kanji. Western names don't lend themselves easily to kanji transliteration, but a service like that helps prevent people from accidentally naming themselves something like "used car lot"