This name can be used as 品 (hin, hon, shina) meaning "article, dignity, goods, refinement."
It can also be used to combine 詩 (shi, uta) meaning "poem, poetry," 史 (shi) meaning "chronicle, history" or 志 (shi, kokorozashi, kokoroza.su, shiringu) meaning "aspire, hopes, intention, motive, plan, resolve, shilling" with 奈 (dai, na, nai, ikan, karanashi) meaning "Nara, what?" or 菜 (sai, na) meaning "greens, side dish, vegetable."
One other form of Shina is made by combining 志 with the phonetic character な (na).
Shina was, at first, uncommon in the early part of the Edo Period (1603-1868), but it became slightly uncommon to slightly common in the latter part of that period and in the first half of the Meiji Period (1868-1912) before it dropped in popularity in the 1900s. This name is still being used today, though it's far more likely that girls named Shina will have their names written as 詩奈, 詩菜, 史奈, 史菜, 志奈 or 志菜 rather than 品 or 志な.