Goldie Wilson II, also referred to as "Goldie Wilson Jr.", was mayor of Hill Valley in 2015. He was the son of Goldie Wilson, who had been mayor from 1979 to at least 1985, and the father of Goldie Wilson III.
In 1986, Goldie Jr. worked at the Hill Valley Hall of Records. On March 3, Marty McFly and Jennifer Parker visited, looking for information that might point them to the location of Doc's secret lab. Marty stated that he (Goldie) was going to become mayor someday, and he was incredulous. Goldie Jr. stated that he knew that, as he has been working his whole life towards that. Marty stated that Goldie's father responded differently when he told him that, and was about to tell him he told Goldie Sr. this in 1955 when he was interrupted by Jennifer. She asked if there was anything Goldie Jr. could do, as Doc was close to Marty, and told him that she was sure he knows what it's like when work takes someone away from them. Goldie Jr. was then sympathetic, and wondered whether the property could have been registered under a different name. 
Since his father was mayor as late as 1985, it's likely Goldie Jr. became Mayor of Hill Valley somewhere in the late 1990s.
The hovering "WELCOME TO HILL VALLEY" greeting sign in 2015 displayed his name ("GOLDIE WILSON jr. / MAYOR") below that of the city, and posters promoting his re-election could also be seen on the walls near an alleyway. 
|Mayors of Hill Valley|
|1885: Hubert - 1931: Jack Thomas - 1955: Red Thomas - 1985: Goldie Wilson - 2015: Goldie Wilson Jr.|