I had submitted a paper to a reputed Computer Science Journal. The reviewer has a lot of constructive changes, in addition to that he also suggested citing a few more papers, all by the same author. Since this is a double blind process, we don't know each other's identity. So, is it common for reviewers to suggest references in this field or any other field ?
I'd say it is a common practice, and I have both been given reference suggestions in blind reviews and given reference suggestions in my own reviews. If you are concerned about a reviewer trying to promote his/her own papers by the suggestions, I'll just say that if the recommendations are apt (i.e., if you read the suggested papers and they do appear to be legitimate references), then it makes sense to cite the papers regardless of whether there is a seemingly disingenuous motive by the reviewer. Even if you don't specifically use the prior work, it makes sense to mention them in your "Related Work" section. If you don't cite the suggested papers, provide a legitimate reason in your rebuttal.
Indeed, if a reviewer is chosen well, he or she should be an expert in the topic of the paper, and most likely does have apt references under his or her name.
It is very common. In fact, some journals explicitly ask the reviewer to answer the question “Are the literature references appropriate and up to date?” (in addition to other reviewing criteria).
Proper citation is an important part of academic publishing, and it should not be treated lightly. It is also the reviewers' job to make sure that you did not, in good or bad faith, forget to cite relevant work in the field. As such, it is common (and desirable) for reviewers to recommend citation of some papers that the authors may have forgotten, or not know of. It has also happened to me in the past, as a reviewer, to recommend deleting some references which I believed were irrelevant or too numerous. (In particular, some overly enthusiastic self-citation or friend-citation).
Now, it may happen that many references you were required to add are from the same author. Maybe it's the reviewer, maybe it's not, but it shouldn't matter to you. Read the papers, and if they're relevant, cite them. If they're not relevant, and you really believe citing them would not be correct, then simply don't cite them and explain your position in the reply to the editor. Don't make accusations (“the reviewer is trying to improve his h-index”), simply state that you do not believe the references to be relevant for reasons X and Y. Remember, the editor is the one making the final decision, not the reviewer!