A quick answer to that question is no.
It is not a requirement that you have your own company to drive for Mover.

In Denmark, you can earn up to DKK 50,000 a year without having to register for VAT. If you have your own company and a CVR number, you must inform us about it so we can settle and handle the VAT with you.

However, there can be a number of benefits for you to have your own business, as expenses associated with driving can be deducted from your income before you pay taxes. You should always check the applicable legislation in the area.

Here you can read more about sharing economy and tax.