Record linkage refers to a range of methods for merging and consolidating data in a manner such that duplicates are detected and false links are avoided. It is crucial for such a task to discern between similarity and identity of entities. This paper explores the implications of the ontological concepts of identity for record linkage (RL) on biomedical data sets. In order to draw substantial conclusions, we use the differentiation between numerical identity, qualitative identity and relational identity. We will discuss the problems of using similarity measures for record pairs and quality identity for ascertaining the real status of these pairs. We conclude that relational identity should be operationalized for RL.