There is no regular meal between those two in American culture.
The basics are breakfast, lunch and dinner.
Some people also use supper along with dinner or in place of dinner.
Breakfast, dinner, supper - especially on Sundays
Sometimes it's breakfast, lunch, supper
There are cultural variations in different regions, but nowhere I know has a meal between breakfast and lunch (or its equivalent noontime meal).
As Doji says, brunch is a midmorning combination of breakfast and lunch, usually only on the weekends and most often at restaurants, in my experience. In my personal experience It's not a standard meal in homes but something for special occasions where you might be getting together with other people.