Fahmida
Yes, it derives from the Arabic root F-H-M (understanding) and aligns with Quranic virtues of wisdom and discernment praised throughout Islamic tradition.
Fahima is the Arabic form; Fahmida is the Persian-Urdu variant with identical meaning but distinct literary history in Indo-Islamic poetry.
While not mentioned specifically, the attribute of fahm (understanding) is praised in numerous Hadith regarding scholars and those who reflect upon creation.
Rare historical records show Mughal-era poetesses and scholars bearing this name, though it remains uncommon in modern demographic registers.
Absolutely, it embodies the Islamic ideal of intellectual pursuit and righteous understanding, representing the seeking of beneficial knowledge.