My understanding is that no you do not.
All you have to do is have a domain name, to use it.
If you want the domain name to be owned by a corporation, or the profits from such to go to a corporation, and so on, then of course you must be incorporated.
Or, you could claim the domain name yourself, then incorporate some time latter, and transfer the ownership of the domain name to the corporation. This takes a lot more work, but it can be done.
But there is no registration of the link, other than one is owned by the other.