Despite an extensive search, the name "Ashmira" (اشمیرا) or "Ashmirah" (اشمیرہ) could not be found in Arabic, Urdu, or Persian dictionaries. The family should be gently advised that rather than keeping this name, it would be better to name the child after one of the Sahabiyat, so that the child may have a connection to that blessed individual and benefit from the blessing of her name.
Allah the Almighty knows best.
Darul Ifta Al-Ikhlas, Karachi.