The disciplinary identity as a computer science student has recently received increasing attention as a well-developed subject identity can help with increasing retention, interest, and motivation. Besides, identity theory can serve as an analytical lens for issues around diversity. However, identity is also often perceived as a vague, overused concept with a variety of theories to build upon. In addition, connections to other topics, such as computer science conceptions, remain unclear and there seems to be little intra-disciplinary exchange about the concept. This article, therefore, attempts to provide a starting point by presenting a so far missing systematic literature review of identity in Computing Education Research (CER). We analyzed a corpus of 41 articles published since 2005 with a focus on the variety of identity theories that are used, the reasons for using them, and the overall theoretical framing of the concept in the CER literature up to this point. We use content analysis with both inductive and deductive coding to derive categories from the corpus to answer our research questions. The results show that there is less variety in the theories than originally expected, most publications refer to the theory of "Communities of Practice". The reasons for employing identity theory are also rather canonical, in particular, there is only little theoretical development of the theories within CER and also only little empirical work. Finally, we also present an extended version of a computing identity that can be theoretically derived from the work in our corpus.