'Team GB' is actually the short form of the name of the UK's Olympic team. The official name is actually: 'Great Britain and Northern Ireland Olympic Team'.
The British Olympic Association started using the brand name Team GB in 1999...

British Olympics Committee issued a statement explaining that the name 'Team GB' represented not only England, Wales, Scotland and Northern Ireland, but also the Isle of Man, the Channel Islands and UK Overseas Territories such as Gibraltar and the Falkland Islands.
These Overseas Territories, it said, are not represented by the name 'Team UK' and would therefore exclude Olympians such as Mark Cavendish, a cyclist who is Manx, and Carl Hester, a dressage rider who from Sark.


Read more: http://metro.co.uk/2016/08/15/rio-olympics-2016-why-is-team-gb-not-called-team-uk-6068065/#ixzz4pdrLdnUkThe