Own your own domain name
As a website designer I often advise business owners who want a website and a domain name for their business to always register it themselves.
Registering a domain name using your own account and being listed as the registered owner and administrative contact is extremely important to ensure that you always have control over your own company domain name.
If, for some reason, you have a website design company or some other person register a domain name on your behalf, it can cause unforeseen problems in the future. If for example, they can no longer be contacted for some reason, whether it's due to poor health, moving away, or going out of business etc., then you could find it very difficult to control what happens to your domain name, especially without some form of proof of ownership. 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 realising or being notified, after a short suspension period the domain name could be purchased by someone else before you get a chance to renew it.
For this reason it's always been my advice to register the business domain name yourself. It's also important to set the renewal of your domain name to 'Auto Renew' within the control panel of your registrar to ensure the domain name does not expire without you being aware of it. You can always change the setting if you do decide you no longer want to retain and renew the domain name.
Two of the registration agents I normally recommend are www.lcn.com and www.123-reg.co.uk