All websites are identified by one or more 'hostnames', sometimes called 'DNS Names', 'Domains' or 'Domain names'. These appear in URLs between the initial double slash and the next slash, so 'www.ucs.cam.ac.uk' in the URL http://www.ucs.cam.ac.uk/managed-web-service.
You don't have a free choice about what hostname to use for your web site.
The University normally uses hostnames that end '.cam.ac.uk'. Within this departments, colleges, etc. use names with their own naming suffixes; for example '.botolph.cam.ac.uk' for the fictional St Botolph's College. The easiest thing to do on the MWS Managed Web Server is to use a hostname with an existing suffex, for example 'project.botolph.cam.ac.uk'. If you want to do this you might want to discuss your plans with the IT staff in the relevant institution.
For testing, there is a special ending '.usertest.mws3.csx.cam.ac.uk' in which you can use any reasonable hostname providing it's not already in use. You should remove such hostnames once they are no longer needed.
New names ending directly with '.cam.ac.uk' are only created very occasionally. This is governed by guidelines overseen by the Information Services Committee. If you think you might be entitled to one, please discuss this with Institution Strategy in University Information Services (email email@example.com). See http://www.ucs.cam.ac.uk/instinfo/domain-names/domainnames for more information.
You can also use hostnames with other endings, e.g. '.botolph.example.org'. To do this you need to obtain the right to use the names, probably by buying it from a 'Domain Registrar'. Domain Registrars normally also provide 'Domain Name System' (DNS) services for the names that they sell. University Information Services' 'Managed Zone Service' may be able to handle this for you, see http://www.ucs.cam.ac.uk/managed-zone-service for further detail.
On the MWS, hostnames are used for two different but related things: