Group names and collective entities

Most of the top premier league football clubs have massive squads of players as well as many non-playing staff. But when 11 members of, say, Manchester United, travel to another team's ground for an away match, we say that Manchester United (not 'some of Manchester United' or 'part of Manchester United') have come to play.
Similarly, imagine a pop group (let's invent one - we'll call them 'The Bloggers') has five members. If one of the members gets sick and the remaining four do a gig, we still say that the Bloggers (not some of the Bloggers or part of the Bloggers) are performing.
If Mr and Mrs Smith and two of their four children turn up at my house I will probably inform my wife that "the Smith family have arrived", rather than denoting them as 'some of the Smith family' or 'part of the Smith family'.
In these cases, a part of the collective entity (team/group/family)possesses all the essence of the whole and (in the case of the football team or pop group) is authorised by the whole to use the official name of the whole.
How far these examples are useful to understanding the Doctrine of the Trinity (by demonstrating that a part of an entity can be legitimately designated by the same term used to denote the entity in its entirety) is debatable, however. I'm not sure we would ever call one footballer by the name of his team or one pop group member by the name of the group. And if Mr Smith popped over for lunch I wouldn't describe my guest as 'the Smith family'. It seems that what these examples consist of is group names, and that such names can be equally applied to the whole of the group or to a part of the group but never to a 'non-group', ie. they cannot be applied to an individual (such as a Person).