Recent studies find increasing evidence for vocal accommodation in nonhuman primates, indicating that this form of vocal learning is more prevalent than previously thought. Convergent vocal accommodation (i.e. becoming more similar to partners) indicates social closeness. At the same time, however, becoming too similar may compromise individual recognisability. This is especially problematic if individual recognisability is an important part of the call function, like in long-distance contact calls. In contrast, in calls with a different function, the trade-off between signalling social closeness and individual recognisability might be less severe. We therefore hypothesized that the extent and consequences of accommodation depend on the function of a given call, and expected (1) more accommodation in calls for which individual identity is less crucial and (2) that individual identity is less compromised in calls that serve mainly to transmit identity compared to calls where individual recognisability is less important. We quantified vocal accommodation in three call types over the process of pair formation in common marmoset monkeys (Callithrix jacchus, n = 20). These three call types have different functions and vary with the degree to which they refer to individual identity of the caller. In accordance with our predictions, we found that animals converged most in close contact calls (trill calls), but less in calls where individual identity is more essential (phee- and food calls). In two out of three call types, the amount of accommodation was predicted by the initial vocal distance. Moreover, accommodation led to a drop in statistical individual recognisability in trill calls, but not in phee calls and food calls. Overall, our study shows that patterns of vocal accommodation vary between call types with different functions, suggestive of trade-offs between signalling social closeness and individual recognisability in marmoset vocalizations.