Do you think green space is a good name for a stonework company?

I would think your company did soft landscaping, not hard landscaping.

Changing the name costs money, and it is a good name. But ask yourself this, is your company a "green" company? Do you do everything environmentally friendly? What about adding some landscaping to your services, like gardening or ponds?

If it's feesable to change the name and you aren't considering adding the garderning services, then maybe reconsider a name to reflect your stone work to really relay your message and attract the right clients, like Corner Stone or something. Be creative and ask your friends and family for ideas.