We consider four different models of process interactions that unify and generalise models introduced and studied by Angluin et al. [2] and models introduced and studied by Mazurkiewicz [17,18]. We encode these models by labelled (hyper)graphs and relabelling rules on this labelled (hyper)graphs called negotiations. Then for these models, we give complete characterisations of labelled graphs in which the naming problem can be solved. Our characterizations are expressed in terms of locally constrained homomorphisms that are generalisations of known graph homomorphisms.