Mitsy,
Technically, no baptists body is a denomination in the traditional sense since all baptist churches are autonomous. Baptist bodies like the SBC were created solely for the purpose of pooling resources (for missions primarily, and also for theological education and publishing). Baptist churches may cooperate with as many of these groups as they wish, since cooperation simply means writing a check to support the various programs of whichever bodies they like.
Consequently, a local baptist church may align itself with as many regional, state, and national groups as it feels are appropriate. Traditionally, a church should not be defined by those associations (since in reality they are - essentially - just charities which they support). Nevertheless, people have started to do so. "Southern Baptist" - for instance - has become an identity in a way that the forbears of the Convention never expected that it would.
Things do become a bit more complicated if clergy wish to be recognized by outside groups (federal chaplains, for instance). To accomplish that goal, some baptist conventions/associatons/groups have taken on denomination-like functions. The ABC-USA, SBC, CBF, Alliance, and Baptist General Convention of Texas all endorse chaplains.
Local churches do not have to affirm the doctrinal stance of conventions which they support, but chaplains do. As a result, chaplains are usually much pickier about where they keep their endorsement. (Mine is with the Alliance - for instance.) Likewise, to my knowledge, you cannot pick more than one endorsing agency.
The short answer then is that, with the exception of chaplains (and - to some extent - other ABC-USA clergy), a baptist makes their denominational affirmation by the local church that they join; not by the cooperative bodies whom they support.
Joshua