I hired a contractor to do some work, the work is complete and I got a
bill.
The amount is $800. On the invoice at the bottom they wrote in ink make
check payable to "john smith", the owner. Not the name of the company.

I guess they are doing this to avoid taxes.

The issue is, I would like to make the check out to the business's name
as
this work involved a permit and was done over a dispute with a neighbor
so I
want a record incase there are any further legal issues between me and
my
neighbor. Should I just make the check out to the companies business or
to
the owner?

I'd make the check out to the company (especially if its listed on the
permit). Thats how I did it with our granite contractor in AZ. They wanted
the check 'personal' to get the cash right away because (I found out later)
the outfit was going out of business and they didn't want to mistakenly
leave any $$ for their creditors. In theory, if I hadn't paid "the company",
I believe there could have been 'creditors' come after me for a 'company'
bill not paid.