How to loop through a list of data frames and assign the numeric portion of the name as a new column value for the data frame?

I have a list of data frames

list.files("data frame - 12345 - App", "data frame - 34567 - App", "data frame - 65849")

Each data frame looks like this

Col1|Col2 |Col3
Row1 Info1 NewInfo1
Row2 Info2 NewInfo2

I would like to add the number portion of the list name as the value for each row of each dataframe's new ID column. All three dataframes should like this

Col1|Col2 |Col3    |ID Name
Row1 Info1 NewInfo1 12345
Row2 Info2 NewInfo2 12345

Col1|Col2 |Col3    |ID Name
Row1 Info1 NewInfo1 34567
Row2 Info2 NewInfo2 34567

Col1|Col2 |Col3    |ID Name
Row1 Info1 NewInfo1 65849
Row2 Info2 NewInfo2 65849

assuming such a list of data.frames

list(App_12345 =data.frame(a=letters[1:3], b=1:3),
     App_12345 =data.frame(a=letters[1:3], b=1:3))
$App_12345
  a b
1 a 1
2 b 2
3 c 3

$App_12345
  a b
1 a 1
2 b 2
3 c 3

you can use

library(tidyverse)
list(App_12345 =data.frame(a=letters[1:3], b=1:3),
     App_34567 =data.frame(a=letters[1:3], b=1:3)) %>% 
  bind_rows(.id = "d") %>% 
  split(.$d)
$App_12345
          d a b
1 App_12345 a 1
2 App_12345 b 2
3 App_12345 c 3

$App_34567
          d a b
4 App_34567 a 1
5 App_34567 b 2
6 App_34567 c 3

By edding a mutate before the split you can transform as appropriate

mutate(d =gsub("App_", "", d)) 

As an alternative you can use purrr's map function like

list(App_12345 =data.frame(a=letters[1:3], b=1:3),
     App_34567 =data.frame(a=letters[1:3], b=1:3)) %>% 
map2(., names(.), ~mutate(.x, d = unlist(str_extract_all(.y, "[0-9]+"))))