To sign on a single van as an independent owner/operator most folks come into the business as a sole proprietor - this means that you just use your social security number for tax purposes. There are many forms of incorporation that are available - although sole proprietorship suits a single truck just fine. I'm not a Lawyer, nor have I stayed at a Holiday Inn Express lately - so I will not even pretend to give you legal advice.
When you sign on with a major carrier, you are leasing your vehicle to that carrier and in turn you are allowed to run under their authority and use the carriers dot numbers. In short, if you are leased to a carrier you are not required to have your own DOT numbers or authority, you run under theirs.
Good luck, I hope this helps - X