shIla in Sanskrit means habit, custom, or nature; by synechdoche, it refers virtue or moral character. As an isolated word, it has not been used, for a long time, as a first name in the few Indian languages that I know. The feminine form, shIlA, is far more common; though I do not know how much the English
Sheila contributed to the rise of the Indian
Sheela, i.e. though, today, parents do connect the name with the Sanskrit word, it is not clear that it was so when the name started being used recently.
Both these masculine and feminine names are attested alone in Sanskrit (see, e.g. Rajatarngini for the male name), but more commonly as compounds with other words (e.g. shIlAditya).