As the abstract makes clear, the finding of Cook et al. (2013) is not really "97% of researchers agree..."; rather, it is "97% of peer-reviewed publications agree". They didn't just go through some directory of climate researchers asking them what they thought. They read the abstracts of all 11,944 publications they found on the topic, and classified them according to what the abstract said. (The classification was blinded and crowdsourced -- read the paper for details.) As a secondary check, they asked the original researchers themselves to evaluate their own abstracts, presumably to control for any bias which Cook et al. might be bringing to the evaluation. The proportions of abstracts endorsing the consensus were 97.1% and 97.2% respectively for the two methodologies.
Note that this isn't asking researchers anything about their own beliefs. Imagine that, for instance, Jane Q. Scientist privately believes that the earth will cool by 5°C in the next century, but that she hasn't found any solid data to back up this belief, so hasn't yet managed to publish anything supporting it. However, in 1998 she published a paper which provided evidence for anthropogenic global warming. Perhaps she now disbelieves the conclusions of that paper, but it remains in the literature because the data and reasoning were strong enough to stand up to peer review, no matter what the original author now thinks. In practice, of course, it's likely that scientists' personal beliefs will be similar to their published results, but I feel it's very important to stress that this study is not an opinion poll -- it's an evaluation of the research itself. (The media can be a little sloppy in their reporting of this distinction.)
Thus, your question is a little misconstrued: we can't answer "Who are the 3%?" because the 3% are research articles rather than people. However, we can ask "Which are the 3% of published research abstracts which do not support the scientific consensus?" And since Cook et al. (2013) is an open access paper with supporting data provided, you can easily answer this question for yourself: simply download the data file from the supplementary data page and look at the papers with an endorsement rating of 5, 6, or 7. (It's in CSV format, so is easy to load into a spreadsheet or text editor.) Further supplementary data is available from the project page at Skeptical Science, and replication of the research is actively encouraged. If you're interested in the actual people behind the 3% of "non-consensus" papers you can look at the author lists for those publications (though of course there's no guarantee that all those authors would still stand by all their conclusions).
I suggest that you start your investigations by reading the paper itself. It's clear and concise, and will give you much more thorough information about the methodology and supporting data than I've been able to fit into this answer.
- Cook, J., Nuccitelli, D., Green, S. A., Richardson, M., Winkler, B., Painting, R., ... & Skuce, A. (2013). Quantifying the consensus on anthropogenic global warming in the scientific literature. Environmental Research Letters, 8(2), 024024.