Beverly Hills attorney Patricia M. Eckert was nominated by Gov. George Deukmejian to a six-year term on the Public Utilities Commission, replacing Donald Vial, the commission’s only remaining appointee of former Gov. Edmund G. Brown Jr. The five-member commission has been dominated by Deukmejian appointees since Mitchell Wilk was named in January, 1987. The nomination of Eckert, 41, a Republican, requires Senate confirmation. Vial, whose PUC term expired, was recently appointed to the state’s Fair Political Practices Commission by Atty. Gen. John K. Van de Kamp.