Personal names are a universal feature of human language, yet few analogs exist in other species. While dolphins and parrots address conspecifics by imitating the calls of the addressee, human names are arbitrary, i.e., not imitations of the sounds typically made by the name’s owner. We investigated the possibility of name-like calls in wild African elephants, a highly social vocal learner in which addressing individual conspecifics could be beneficial. Using random forest models, we found that calls were specific to individual receivers, even when acoustically divergent from the receiver’s own calls. Elephants differentially responded to playbacks of calls originally addressed to them relative to calls addressed to a different individual, indicating that elephants can determine from a call’s structure if it was addressed to them. Our findings offer the first evidence for arbitrary naming of conspecifics in nonhuman animals.