The 49-year-old actress recently made a return to the social networking site under her married name, but following her split from husband Ashton Kutcher in November 2011 she wants to have a new moniker.
She wrote: "Time for a change, twitter name change ... any suggestions? (sic)"
Celebrity interviewer Piers Morgan suggested she changed it to "mrsmorgan", but Demi laughed it off insisting the title was already taken by Piers' wife, journalist Celia Walden.
She wrote: "I think that one is taken! RT @piersmorgan: How about mrsmorgan ? (sic)"
Demi has previously been a prolific user of twitter, but stopped using the site in January 2012.
Last month, the 'Indecent Proposal' actress left Utah's Cirque Lodge clinic - where she was receiving treatment for "an eating disorder and addiction issues" - and is said to now be in a "much better place".
A source previously said: "Demi is in a much better place. She has been working on herself a lot. She is content.
"Demi feels great and she is eager to get back to work. She has been focusing on her health in the last month and she's getting better every day. Demi wants to work again; she knows that she can handle a few projects so she's looking forward to that."