I graduated in 1979. The girls didn’t have any teams back then unless you were on the cheerleading, flag twirling or dance team squads. And those just performed before/during the boys’ teams games. I think there were only intramural type teams for girls at that time.
The university’s teams’ name is the Bulldogs. The women’s hockey team is called the Lady Bulldogs. An area college teams’ name is the Lumberjacks. They call their women’s teams the Lumberjills!
My HS was all boys then (it has since been made coed by court order), but I don’t think out teams had any nickname, certainly none that comes to mind.
In the case of both high schools “Lady” was added before the name for football and basketball (possibly others) but basically the same name.
(60s and first half 70s)
+1 for a “Lady” prefix at my school. A quick check of the athletic program’s twitter feed shows that this is still the practice.
We were the Hornets and the Lady Hornets. I find it interesting that the distinction still exists when (AFAIK), the practice is practically unheard of at the collegiate level.
Mine had a non-gender-specific animal name for both sexes.
School mascot was the “Horsemen”. Women’s teams were, I shit you not, “Lady Horsemen”.
Cocks? Titmice? Boobies? 
Bears.
Spartans and Lady Spartans. Not very creative, but what can you can do.
In the town where I live now, the team is the Blue Jays, and the girls’ teams are called the “Lady Jays.” I think they should just drop all pretense and call them the va-jay-jays 
Guys were the Panthers, girls were the Lady Panthers, and the band was the Marching Panthers.
Interesting. It seems like a different name is rare- and I guess it would be based on my experience.
But yes, separate names for the boys and girls across all sports as my high school had and still have the Bucks and the Gazelles. It worked well- and back in the day homecoming was known as Arickara days complete with Native American headgear and outfits for the homecoming court. It looks like they have converted that tradition to a Pioneer Days and settler themed event now.
Both teams at my school were the Monarchs.
Carlsbad, New Mexico High School is the Cavemen and Cavegirls. Why not Cavewomen?
Bulldogs for all the teams, though youth wrestling was Bullpups. The HS marching band was the Scarlet Regiment, and the MS marching band had it’s own name, too. The marching band was also the only “team” that won anything in the fall, until the cross country team came under the leadership of yours truly.