In general, an adult who wants to change their name can file an Application for Change of Name, along with an Affidavit, with their local Probate Court. The Probate Court publishes a pamphlet on the Procedure for Applying to the Probate Court for Change of Name, which provides a overview of the process.
According to Connecticut General Statutes sec. 45a-99 "(a) The courts of probate shall have concurrent jurisdiction with the Superior Court, as provided in section 52-11, to grant a change of name, except a change of name granted in accordance with subsection (a) of section 46b-63..."
As noted in the statute cited above, there is an alternative procedure for requesting a restoration of your maiden name after a divorce. For more information, see CTLawHelp's guide on How to Get Your Maiden Name Back After a Divorce.
More questions about Connecticut law on names and name change? Then visit our Law about Name Changes page for links to additional legal references and resources.