Answer:
Yes, her name was Lisa Giocanda(sp?), it is now believed her husband had commissioned her portrait because they had just had a baby. The painting was never finished, but you can kind of see going around her neck is a white scarf, which was a cultural symbol for having successfully given birth, they didn't have hospitals and modern medicine, so a lot of women died giving birth.
Another sign that she had recently given birth is her hands, they are puffy. Sometimes women have water retention problems when they are pregnant, and the Mona Lisa's hands are probably puffy as a left over result of that.
A lot of people assume and believe she had an affair with Da Vinci, which is completely bogus. She was an intelligent woman and Leonardo enjoyed her company, they apparently had some pretty great conversations, but they never had a sexual relationship. Leonardo da Vinci was homosexual.
When he stopped working on this piece, he never gave it to the man he commissioned it for because he liked it so much.(he did this a few times, and had a lot of trouble finishing commissions) Instead he kept it and brought it with him wherever he moved, which is why it ended up in the Louvre in Paris, even though it had been painted in Florence, Italy.