By Popular Demand...
Many a friend of mine has investigated what their "Russian" name is through a fun website and have started wondering what mine is. No offense to random-generation programs, but I thought I'd use the chance to talk about how Russian names are generated in real life. :)
The first name, like in the States, is given. My given name is Erin; the closest Russian equivalent is Irina. If you want to look up the closest thing to your given name in Russian, a good list of common Russian names is here. The list also includes diminutive forms for names that have them; this is basically a nickname. Just as someone would call Jonathan "Jon," in Russian, "Aleksandr" becomes "Sasha." The diminutive form of Irina is Ira.
The Russian middle name is patronymic- your father's name with a suffix meaing "daughter of" or "son of." Women use the suffix "ovna", men use the suffix "ovich." So my patronymic middle name would be "Leonovna."
Last names, or surnames, are either the same as one's parents, or taken from a husband when married as they (usually) are in the US. They too have suffixes which change for men and women; common endings are -ov (-ova for female), -ev (-eva) and -in (-ina). As in many other countries, the roots of surnames often lie in one's ancestry (such as "Anderson," meaning "Ander's Son") or traditional family occupation (such as "Smith"). Since my ancesters in the States were farmers for many generations, my surname could be "Farmerova."
So, all combined, my Russian name is: Irina Leonovna Farmerova. But you can just call me Ira. :)