These cookies called ladyfingers because their shape literally resembles fingers and they are also called sponge fingers now that reasoning I do not know.
Lady fingers is called that because of its shape. It resembles a woman’s finger which is thin and delicate, just like the light French biscuit is designed to be.
This is due to its adoption of the fingers of the ladies. Things are usually named with a meaning and that's it. Hence anything beyond this is hard to decipher.
Some people might call this finger because it is smooth and instead of one or two fingers, it has a hand-like feature. Others might call it because it is so close to the hand.