Pseudonym is a fictitious name or a professional name or any other name which is not the original name of an Individual. Such name is protected under Trademark.
Trademark means the protection against the illegal use of any name, symbol, mark, logo, shape of goods, etc which creates the brand. While the copyright is for the protection of literary work, music, dramatic and artistic works. Hence the Pseudonym is protected under Trademark.
To know more about Trademark and copyright refer the blog IPR in India: Difference between Copyright, Patent & Trademark