Sheenah \she(e)-nah\ as a girl's name is a variant of Sheena (Irish). See for meaning of Sheenah.
The baby name Sheenah sounds like Sheina, Shainah, Shaena, Shannah, Shanah, Shawnah, Shaunah, Shaynah, Shena and Shonah. Other similar baby names are Sheenagh and Sheelah.