"We don't want to be left behind," college spokeswoman Valerie Owens said.
"I think this is of critical importance to the Eastern Panhandle," added Del. John Doyle, D-Jefferson, who works on higher-education issues in the Legislature.
Shepherd College can seek the name change since four-year colleges were given the permission to request university status in the last session of the Legislature.
The state Higher Education Policy Commission developed the requirements for university status, which includes offering graduate programs and having several program accreditations, Shepherd officials said.
Shepherd College has been increasing its graduate study programs, and this fall it began offering a master's degree in curriculum and instruction through its education department.
Dunlop said the name change will not require significant staff increases or costs.
To get input on the proposal from students, staff and the community, Shepherd officials have scheduled open meetings on Oct. 21 and 22 in the Frank Creative Arts Center recital hall, room M08. The meeting on Oct. 21 will start at 11:30 a.m. and the meeting on Oct. 22 will be at 4 p.m.
After the discussions, Dunlop is expected to seek approval for the name change from the school's Board of Governors, according to a press release from the school. The Board of Governors' recommendation would be sent to the Higher Education Policy Commission, and then the name change would have to be made in the Legislature, the release said.