According to a legend, Lord Shiva once pinched off one of the heads of Lord Brahma to arrest His pride. The kapalam or head got stuck on Shivas hand. A crestfallen Brahma came to this place, installed a Lingam and did long penance. This Lingam is worshipped as Kapaleeshwarar (named after the kapalam incident). Since Devi Parvati did penance here as a peahen, the place came to be known as Mylapore (a place connected with peahen or mayil in Tamil).
Heres another belief about the name Mylapore. Once when Devi Parvati was listening to Lord Shiva narrating the significance of the Panchakshara Mantra (Na-Ma-Si-Va-Ya), the Goddesss attention was distracted by a dancing peacock.
The Lord got angry, cursed Parvati to transform into a peahen and do penance at this place, then known as Kapalinagar. Parvati came here, did severe penance and got rid of the curse. Later She united with the Lord. Some believe that the association with peahen or mayil gave the place its name Mylapore.