Please see this page for the meaning of Aleena according to the Quran: Aleena
Some Islamic sites say it means "good-looking" or "light". This is incorrect as this is the non-Islamic meaning of the name. Aleena is a variant of Alina and both mean "light" or bringer of light in Greek. In Celtic it means good looking.
I couldn't find any reference to the "silk of heaven" meaning in any trustworthy Islamic sources.