All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
It is permissible to name your daughter with this name as this name is not exclusively for males; it means either of the following: (a) the opposite of Maymanah (the right side), or (b) ampleness and richness. Al-Jawhari said in his book As-Sihaah: “Al-Maysarah is the opposite of Al-Maymanah (right side), and it also means plentifulness and richness.”
Some women were given this name, they were only a few; Abu Nu’aym mentioned in his book Ma’rifat As-Sahaabah a female narrator whose name was Maysarah bint (i.e. daughter of) Habashi At-Taa'iyyah [from the tribe of Banu Tayyi']. Besides, Ibn ‘Asaakir said in Taareekh Dimashq: “‘Ataa’ ibn Abi Rabaah, and the name of Abu Rabaah is Aslam, who was the servant of Habeebah bint Maysarah bint Abu Khuthaym.”
Allaah knows best.