When will my baby know who I am?

They already do! They may not be able to call you by name, but infants have an awareness of their mothers from in utero. Your voice and feel and smell make you "known" pretty much right out of the starting gate!
Subjective. But I have had mom's tell me within days or weeks. Their vision is poor initially, but they can hear, feel and smell, and familiarity of all of these factors strengthen the mother infant bonding. Breast feeding enhances this even further.
Immediately. Your baby knows you based on your scent, and sound. Even before birth your baby spent months listening to mother's and father's voices, coughs, and home sounds such as the music that you listen to. Your baby will be attuned to mother's scent, especially if nursing. So, the answer is, your baby knows you at birth.