It's about the brand and personality and the perception you want to convey. Brown-Smith Web Services sounds like you're not very creative.
It's about people being able to remember it.
It's about the URL.
It's about being happy with it since hopefully you'll have to live with it for a long, long time. You don't want to have to change it.
The name does matter but it shouldn't make or break your company. But everything has an impact, big or small.
For a marketing firm I created with a friend we just took half his last name and combined it with half my last name and added "Group" at the end. Took us a few minutes to figure that out. URL available. People loved it, constantly questioned what it meant so they remembered it. Loved the story of how we created it. It didn't sound stodgy or boring...we were a marketing firm so we wanted to convey creativity.