The word "Rameen" (رامین) appears to be the plural of the Arabic word "al-rami", meaning "archers" or "those who shoot arrows." On this basis, it is permissible to name a boy Rameen. However, since this name appears in books as a male name and its grammatical form is masculine, a different name should be chosen for a girl instead of Rameen.
Allah the Almighty knows best.
Darul Ifta Al-Ikhlas, Karachi.
المنجد: (مادہ: ر-م-ی، ص: 374، ط: مکتبة الحرمین)
الرامی: فا، ج: رماۃ و رامون، تیر مارنے والا
القاموس المحيط: (1201/1، ط: مؤسسة الرسالة)
والحسن بن الحسين بن رامين : فقيه.