We had a case about a year ago where we got 'domain dispute' documentation sent to us from a supplier who wasn't too happy that a few years prior we'd registered a domain name which was the same as their company. I gather the MD had previously told them they could buy the domain off them, though the opted to contact Nominet in regards to the name. In the end we did hand the domain over to them, I think not so much due to that but as the supplier threatened to dramatically reduce our trade discount.
We do have a few other domains with names matching the supplier, however we're UK distributers for those companies and they're non-UK based the relevant suppliers don't mind.
Personally where possible I'd always register the domain name myself, thus avoid the
website hosting designer from running off with the domain name. That way I can ensure the domain name has the correct ownership details and can switch DNS if needed.