There are two reasons a web designer would register a domain name under their own control. The honorable reason is to protect the client from all the fraudulent "renewal notices" that come from companies that have nothing to do with the domain registration. In this case, they are protecting the client from falling for scams. The second reason is not so honorable, and I try to warn people about it. If the designer does this strictly to hold the domain name hostage, there is little that can be done. Technically, that designer owns it, and if they are unreachable, this is just as much a scam IMO as those who good designers are trying to protect their clients from.

I don't know which is the case here, and I hope it works out well for your client, but this is an issue that needs to be openly discussed so that it will hopefully serve to inform other business owners to beware of this type of danger.

Fortunately, there is now a way to register domain names "privately" so you don't get so easily hit with fraudulent domain renewal notices. This also means that you don't have to rely on the honorable intentions of your web designer. This may or may not be directly helpful in your current situation, but I believe it will be very helpful to others reading this thread. It could even prevent someone from having this happen in the first place.