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."
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