As a web designer who also provides a web hosting service for their clients, I often advise business owners who have not yet registered a domain name to always register it themselves.
Having the domain name in your own account and being the registered owner, administrative and technical contact is vital to ensure that you always have control over your own domain name.
If, for example the person who registers a domain name on your behalf is no longer contactable for whatever reason i.e. poor health, moves away, goes out of business etc., then you may find it extremely difficult to control what happens to your domain name without some form of proof of ownership, and even then the process of taking control of the domain name can be fraught with difficulties.
Worse case scenario is that if your domain name expires without you being notified or aware of it's expiration and subsequent suspension, the domain name could be purchased by someone else before you get a chance to renew it.
My advice is always register your business domain name yourself. But also remember to set the renewal of your domain name to 'Auto Renew' to ensure the domain name does not expire without you realising it.
One of the best registration agents I normally recommend is www.123-reg.co.uk
