This is a tricky question Ivarr. It seems the term "Alamanni" was being applied to people in what is now south west Germany for some centuries before we can say a 'tribe' of that name came to exist. And your point about the various 'kings' of the Alamanni mentioned in Roman sources and the likelihood that this means the early Alamannic Federation was a loose one is important to remember.

The overlap between the "Alamanni" and the "Suebi" is also both interesting and puzzling. The "Suebi" seem to have been more of a loose federation or linked league of tribes, probably connected by common religious traditions. The people who called themselves Suebi who later crossed the Rhine in the Fifth Century and joined the Alans and Vandals on their trek through Spain to Africa were probably from tribes who belonged to this tradition and used "Suebi" as a common designation rather than people from a single tribe which called themselves the Suebi.

In the case of the Alamanni, it could be that when the various tribes of this region combined warbands to go on an extended raiding expedition or campaign they called themselves "all the men" - ie the united warbands of the Juthugi, Bucinobantes etc.

It may be that, later, as this kind of co-operation became more common, the pickings over the border got easier and neighbouring tribes began uniting as well (eg the Franks) this loose federation became slowly tighter, until the name referred to a larger federated tribe rather than an opportunitistic collection of warbands.
Cheers,

Thiu