I'm in the same position as you, set-up as a self-employed web/graphic designer in January. But to be honest I actually didn't find it to be a handicap that people knew I was a one-man-band.
If you want you can refer to your design company as a 'business'. That way you're not doing anything wrong, as you have registered a 'business' name, and are conducting 'business' under that name.
Best of luck with the venture!