It seems to be common. Even the Wikipedia article references this trend for those who have multiple genders. It's just easier to refer to your different sides by a name. I tend to say "Cailan is my guy side, Jade is my girl side, and together they make me (my birth name, which happens to be unisex)."
I personally began simply referencing them by the names of two characters in a book as being representative of who my gender personalities were. Eventually I decided I didn't want to use specific characters, and picked names for each of them, much like MtFs and FtMs pick new names for their new genders. It was important that each was to a degree unisex, but each name would lean in a different direction. Cailan is old Celtic and depending on the spelling can go either way, but most uses are masculine. Jade tends to be thought of as a feminine name, but there are a lot of male Jades out there too (according to the US Census Bureau, nearly as many as females).
Long, long before I realized I was trans/bi-gender, I had a tendency to try on other names. I knew my name didn't fit, quite, but I had no idea why. It drove my mom nuts. Now I tend to be overly sensitive to name change because I did it so often as a kid/young teen it became a source of irritation from my friends and relatives. Therefore I'll probably just stick with my given name for general purposes. Plus legal name changes are a lot more painful and difficult once you're a "mature" adult and have mortgages, credit ratings, contracts and a known career name to deal with. Powerful people know and trust me professionally as AJR and will answer their phone with certain expectations. The same people might not even take a message from CJR.
