To obtain a legal name change in Vermont, an applicant must submit a petition to the court. No publication is required. Registered sex offenders may not be eligible to change their name unless the court finds a compelling purpose. (Vt. Stat. Ann. tit. 15, § 811 to § 817 (West))
For instructions on legal name changes for minors under 18 in Vermont, see NCTE's Name Changes for Minors in Vermont resource.