What if your reviewer told you need to cite author A and Author A is you? It is common practice in my field to remove self-citations completely in a manuscript for consideration. Even if you use neutral language like: “Author A said XYZ” (with Author A being myself), it is frowned upon. One of my senior colleagues was telling us she got a review that said she needed to read more works of Author A and cite Author A more and her not mentioning her shows a distinct lack of the literature! (She is Author A.)

This is quite an amusing situation but while it is under revise and resubmit still, she is considering withdrawing it and submitting elsewhere because saying “Hey, I am Author A and I think I know my own work quite well” wouldn’t really cut it, right? How would you respond to this largely negative review without compromising anonymity? Or would you just let the editors know?
If it's a wide practice in your field to remove self-citations at the submission stage, and a well-known practice, then reviewers should be aware that the conscious omission of author A should be a sign that author A might be an author of the work under consideration. This suggests that the reviewer may not be aware of the convention—perhaps it was written by someone relatively new to your field.

I would just proceed by incorporating the comments, and explaining to the editor why you broke with convention.