The instructions to the Form 990 say that it must be signed by the current president, vice president, treasurer or other authorized officer.  It doesn’t say anything about how they must sign.

Considering that so many signatures are illegible and that some documents can be valid if signed only with an X, I doubt that the IRS would refuse to accept a return signed by Lady Gaga instead of by Stefanie Joanne Angelina Germanotta.  And I am pretty sure that filing with a stage name would not eliminate the concept of perjury if the return was signed by someone who knew it was materially wrong.