Van Halen parted ways with original vocalist David Lee Roth for the first time in 1985. Roth's position was filled in for by Sammy Hagar that same year, and Hagar would go on to front the ban until 1996.
According to ex-bassist Michael Anthony in an interview with Steve Gorman Rocks!, basically everyone surrounding the band wanted them to change their name when Roth quit. Anthony said the Van Halen brothers weren't interested and obviously it never happened.
"We had everybody — Warner Brothers, our management, our lawyers — going, 'Oh my God. David Lee Roth's gone.' They thought that that was such a strong identity. Warner Brothers wanted us to change the name of the band. I remember Eddie and Alex, we were at Warner Brothers, and they were yelling, going, 'Hey, hey, this is our last name. This is our careers. And we're Van Halen.'"
After a while, Roth would return in 2007 and stay until the end of Van Halen.