Is it permissible to register in forums and social media sites under a male name, while the female speaks as herself and reveals the truth when asked?

A woman's participation in forum discussions is not permissible except out of necessity and within the bounds of Islamic regulations. There is no harm in registering with a male name if participation is permissible, as long as she does not intend to deceive or imitate men. However, it is preferable to choose a name that indicates she is a woman.