It doesn't really matter provided you're only going to be operating in a small locality.
"Reflections Window Cleaning" is registered by Paul J Smith in Somerset, but I've lost count of the number of other "Reflections..........." I've seen around, including several who post on here :

If you started trading in the same area as the rightful owner of the name, he/she would probably contact you and demand that you stop.
For example: a second hand shop near me started up, calling itself "'Arrods". The real Harrods got to hear of it and threatened lega action. The local shop responded by changing its name to "Not 'Arrods"
