Everywhere I have worked we have moved from short names to the full organisational name in the web address. The aim is to build identity with the organisation and make people more aware of the name. It has worked.
Short web addresses used to be commonplace when you had to type them in, but these days initial jumps to site are often through thinks like Google and browsers remember addresses so there is really no need to ever type a long name again.
I much prefer the full web address britishairways.com, althought the term ba.com has become useful currency to refer to the web site.