Since there are no Medieval Italian or Medieval Tuscan names starting with Q, today is a wildcard. I made sure not to repeat any of the Medieval Q names I used in my 2018 post.
Qaliyun (Mongolian) means “otter.”
Qongqor (Mongolian) means “chestnut” (the horse colour).
Quant (Scandinavian) derives from the Middle High and Middle Low German word quant (trickster, imp, rogue, prankster, smart-aleck).
Quiryn (Dutch) is a form of Quirinus, which possibly derives from the Sabine word quiris (spear).
Qasmuna (Moorish Arabic) means “to divide, to distribute.”
Quenylda (English) is a form of the Anglo–Saxon name Cwénhild, derived from Old English roots cwén (woman, wife) and hild (battle, war). My 2018 post on Medieval names included the forms Quenilla and Quenilda.