Depending on the context, I introduce myself as a sociologist, a professor, a criminologist, a law and society scholar, a punishment and society person, or, if I'm feeling particularly feisty, a sociologist with a specialization in criminology in the tradition of law and society scholarship. I think part of this comes down to context--how much detail does the audience want/need? And some of it is about the institutional homes of our training and current job--my Ph.D. was interdisciplinary, but housed in sociology, and I currently work in a sociology department, so that feels like it ought to be my primary identification. Sociology also best describes my general intellectual orientation in how I approach social science questions. Yet that label sometimes chafes because "mainstream" sociology often pays so little attention to the kinds of topics I tend to pursue.
Criminology should be an obvious label, and yet I hesitate to use the label of criminologist in isolation. I think this is in large part because criminology has become a discipline more interested in predicting crime and the individual-level correlates of criminal justice contact, instead of punishment as a social institution. In addition, as criminology schools increasingly became training schools for professionals working in the criminal justice system, professors (and graduate students) in those programs increasingly pursed research about how to best operate that system rather than more radical critiques. You can see these trends reflected in the annual meetings of the American Society of Criminology, papers in the flagship journal Criminology, and the research interests of faculty at criminology programs. Although there is a new generation of scholars working to place sociological punishment research back into the core of criminology, they still are a minority (albeit a high-status minority in many cases).
Which takes us to law and society. Bringing together legal scholarship and social scientists, the Law & Society Association and related interdisciplinary socio-legal journals have become the favorite home for many punishment folks. Indeed, what I recognize as my core subfield--punishment and society--explicitly references this intellectual home. And so it is at those meetings, and in those journals, that I most frequently find the most interesting and relevant (to me) research. Yet if you tell the average person (or even sociologist) that you are a "punishment and society scholar," you are likelier to get a blank look than if you say "I'm a criminologist."
Sometimes I think all of us working in sociology on questions of social control and punishment ought to loudly proclaim ourselves "criminologists" to wrest back that label. The study of crime and punishment always needs both perspectives--understanding patterns of criminal behavior should not be separated from the broader history of how we came to call certain acts criminal and how we adjudicate and punish such behavior. Like the loose collection of topics organized under the banner of law and society, I would like to see a criminology that was less a firm discipline and more a big tent of people working from different intellectual starting-points.