Sireen is a non-Arabic name. It is the name of the sister of Prophet Muhammad's wife Marria al-Qibtiyyah. She is aunt of the Prophet's son Ibraheem, and wife of Hassaan ibn Thabit, an important companion of the Prophet (saw). This is the reason why it is used by Muslims.
The actual word might come from either ancient Greek or Persian. In Greek it could be a reference to the Sirens, mythological sea creatures, and in Persian it could mean flower, mountain top, or satiated (opposite of hungry), but these meanings aren't certain since the historical Sireen mentioned above came from Egypt.
Sireen can be used by Muslims since it is a sahabiyyah's name. If someone had an inappropriate name when converting to Islam, the Prophet may the peace and blessings of God be upon him, used to ask them to change their names to a name with a better meaning. But the Prophet didn't ask Sireen to change her name, which means it is a good and acceptable name for Muslims.