I am starting a small business and have decided on a name (I Hope). I
know that the county where I will file the DBA has a website listing
all of the businesses registered in the county.

http://www.co.san-bernardino.ca.us/acr/fbninfo.htm

If there is a business with my desired name I can't use it, which
makes sense. Is there a similar service at the national level? Will
there be a problem if the name of my business is the same as another
company somewhere else? For example, I'm sure that I can't name my
company Microsoft, but where would I find out about this type of name
conflict?

I would go for 'Microsoft', it's got a nice ring to it and I am sure
you could soon make it your own.

Try " Gatesland" or "Billsworld"

Steph53