Two-flowered violet

[JennyS]

I came across this Common Dog-violet today, and wondered if theres a name for when one flower is growing out of the centre of another?

[Tiggrx]

You can buy varieties of Primrose and Monkeyflower (and probably other plants where one flower grows out of another. These are referred to as "Hose in hose".
However, in those cases it is because the sepals are deformed and look like petals hence appearing as two flowers. In your picture the violet has petals and sepals on both flowers so it appears that there really are two flowers.