[Watson + Nowlin]

From the point of view from a customer, I would stick with Construction by Design, or at the very least have remodeling in the name but not supply. Placing supply in there will make customers think you are selling supplies to remodelers, contractors etc.

Now, if you were to create a DBA for contractors supply might be fine. However, like your consultant suggested, it is better to keep everything under one roof.

That said, the business name matters a lot.