Yes. They simply need to fill in this form and send it, with the £25 fee, to the Electoral Commission: https://www.electoralcommission.org.uk/sites/default/files/electoral_commission_pdf_file/form-rp2.pdf (In practice the wording of the party's constitution might require them to hold an Extraordinary General Meeting of their members...
(In practice the wording of the party's constitution might require them to hold an Extraordinary General Meeting of their members first, in order to approve the application for a name change).