I don't run a production company, so take this for what you will.
I am against putting a personal name in a production company for two reasons:
1. It give clients the perception that you're bigger than you may be. Bigger=more resources.
2. It's easier to either have someone else run the company once it reaches a certain size or simply sell the company if you're no longer interested in running it.
That said, in smaller markets maybe having your name in the business name helps in that your reputation is widely known so attaching that reputation to your business becomes important.
Honestly, I don't think there's a right or wrong anser to this one.
