Before ordering the name of any public street or private easement changed upon the petition filed as hereinabove stated, the City Council may, at its discretion, adopt a resolution of intention declaring that the public interest and convenience require that the name of the public street or private easement described in any such petition be changed. Such resolution shall designate the street or easement, the name of which is intended to change, shall describe said street or easement by reference to other streets or easements parallel thereto, and shall set forth the name or names which it bears or by which it is commonly known, and shall state the name to which it is proposed to be changed. Said resolution or intention shall be posted in the three (3) public places designated by the resolution of the City Council. At the expiration of ten (10) days after the resolution of intention has been posted, if no written objections to the proposed change of name shall have been filed with the City Clerk as provided in this Chapter or immediately upon the overruling of said objections by the City Council, the City Council may pass a resolution ordering the name of the street or private easement changed as contemplated in the resolution of intention.