So far, the distributed computing community has either assumed that all the processes of a distributed system have distinct identifiers or, more rarely, that the processes are anonymous and have no identifiers. These are two extremes of the same general model: namely, n processes use l different identifiers, where 1 l n. We call this model homonymous model. To determine the power of homonymous model as well as the importance of identifiers in distributed computing, this thesis studies the consensus problem, one of the most famous distributed computing problem. We give necessary and sufficient conditions on the number of identifiers for solving consensus in a distributed system with t faulty processes in the synchronous case. We show that in crash, send omission and general omission failures model, the uniform consensus is solvable even if processes are anonymous. Thus, identifiers are not useful in that case. However identifiers become important in Byzantine failures model: 3t + 1 identifiers is necessary and sufficient for Byzantine agreement. Surprisingly the number of identifiers must be greater than n+3t 2 in presence of three facets of uncertainty: partial synchrony, Byzantine failures and homonyms. This demonstrates two differences from the classical model (which has l = n): there are situations where relaxing synchrony to partial synchrony renders agreement impossible, and, in the partially synchronous case, increasing the number of correct processes can actually make it harder to reach agreement.