labels on a stacked density plot

I'm generating a stacked density plot:

ggplot(data=tydy_rawdata, aes(x=timepoint, y=tpm, group=fct_inorder(names), 
    fill=fct_inorder(names))) +
         geom_density(position="fill",
                      stat="identity") +
         scale_fill_manual(values = rev(mycolors))

plot :

I would like to add label on each curve (or at least the top 3 or 4) basing on the "names" displayed on the right.

I'm trying adding geom_text but the result is this :

gplot(data=tydy_rawdata, aes(x=timepoint, y=tpm, group=fct_inorder(names), 
    fill=fct_inorder(names))) +
         geom_density(position="fill",
                      stat="identity") +
         geom_text(aes(label=names)) +
         scale_fill_manual(values = rev(mycolors))

plot :

Are there some way to do it?

First, your chart is a stacked area chart, i.e. geom_density with stat="identity" is equal to geom_area. Second, when adding labels via geom_text you have to take account of the position argument. As you use position="fill" for your density/area chart you also have to do the same for geom_text.

As you provided no example data I created my own to make your issue reproducible:

library(ggplot2)
library(forcats)

set.seed(123)

tydy_rawdata <- data.frame(
  names = rep(LETTERS[1:10], each = 6),
  timepoint = factor(seq(6)),
  tpm = runif(6 * 10, 0, 80)
)

ggplot(data = tydy_rawdata, aes(
  x = timepoint, y = tpm,
  group = fct_inorder(names), fill = fct_inorder(names)
)) +
  geom_area(
    position = "fill",
    color = "black"
  ) +
  geom_text(aes(label = names), position = "fill")