You would have to provide a labelling function to the labeller
argument in facet_grid()
, which uses a named character vector as lookup table.
library(ggplot2)
ggplot(mpg, aes(displ, cty, fill=cyl)) +
geom_point() +
scale_fill_continuous() +
facet_grid(rows = vars(drv),
labeller = as_labeller(c("4" = "Case1", "f" = "Case2", "r" = "Case3")))

Created on 2020-05-28 by the reprex package (v0.3.0)
EDIT:
To use an extra strip layer as a spanning title, you could use facet_nested()
from ggh4x (full disclaimer: I build that package).
library(ggplot2)
library(ggh4x)
ggplot(mpg, aes(displ, cty, fill=cyl)) +
geom_point() +
scale_fill_continuous() +
facet_nested(rows = vars("title", drv),
labeller = as_labeller(c("4" = "Case1", "f" = "Case2",
"r" = "Case3", "title" = "My Title Here")))

Created on 2020-05-28 by the reprex package (v0.3.0)
If you don't particularly care about the strip being there, you could use a secondary y-axis guide.
library(ggplot2)
ggplot(mpg, aes(displ, cty, fill=cyl)) +
geom_point() +
scale_fill_continuous() +
facet_grid(rows = vars(drv),
labeller = as_labeller(c("4" = "Case1", "f" = "Case2", "r" = "Case3"))) +
guides(y.sec = guide_none("My Title Here"))

Created on 2020-05-28 by the reprex package (v0.3.0)