merge multiple dataframes and give a title for each dataframe in R

Question

I have a question for rbind in R

I have multiple data frames

df1 <- data.frame (first_column  = c("1", "2"),
                  second_column = c("3", "4")
)

df2 <- data.frame (first_column  = c("1", "2"),
                  second_column = c("3", "4")
)
df3 <- data.frame (first_column  = c("1", "2"),
                  second_column = c("3", "4")
)

I would like to merge these dataframes but separate them with a title, the results would be:

  first_column second_column
df1
1            1             3
2            2             4
df2
1            1             3
2            2             4
df3
1            1             3
2            2             4

I have tried rbind, I know I could manually insert df_name one by one, but if I have more than 10 dfs, that would not be feasible.

Thank you very much