@Garrett
No, it's a reference to the statue.
In the Birth of Venus, she's looking forward with her head tilted to the left (her right), is covering only her right breast, and is covering her crotch with her hair.
In both this and Venus de' Medici, she is looking to her left, covering both breasts, and not covering her crotch with her hair.
Also, her fingers more closely match the Venus de' Medici (gap between right pinky finger and other fingers, gap between left middle and ring fingers) than the Birth of Venus, though the match isn't perfect.
As an addendum, I have now used the word crotch on this site three more times than I am comfortable with, and spent way too much time studying a the fingers on a statue.
Also, I knew it was a reference to the family, I was just wondering why there was a seemingly needless apostrophe (I'm more familiar with French than Italian, and in French it would be "de")
Though thank you for explaining it to me, I was unaware that it was short for "dei"
@squerl
Thanks for explaining it to me.