"Eezil" (اِیْزِل, with a fatha on ہ, a sukoon on ی, and a kasra on ز) is an English word meaning "a wooden stand used to hold a painting or picture". Given this meaning, the name is not appropriate. It would be better to choose a name from among the names of the Azwaj Mutahharaat or the Sahabiyat (may Allah be pleased with them all), or to select any other name with a good meaning.
Allah the Almighty knows best.
Darul Ifta Al-Ikhlas, Karachi.
سنن ابی داؤد: (رقم الحدیث: 4955، ط: دار ابن حزم)
عن أبي الدرداء قال: قال: رسول اللہ صلی الله علیه وسلم: تُدعون یوم القیامة بأسمائکم وأسماء آبائکم فأحسنوا أسمائکم․