how to pass the name of dataframe list inside a list using a loop in r

Your code produces a list of length 3, the number of iterations, and each of the three list items is again a list of length 3, the number of dataframes in mydflist. But from the formulation

What I want to do is to access to the results of each dataframe by adding the ith number of iteration, something like: results$mydflist$myfirstdfi where i will be the number of iteration so results$mydflist$myfirstdf1.

in your question I guess what you really want is a flat list of length 9, containing one item for each each iteration step and each dataframe in mydflist, named

"myfirstdf1" "myseconddf1" "mythirddf1"

"myfirstdf2" "myseconddf2" "mythirddf2"

"myfirstdf3" "myseconddf3" "mythirddf3".

The following function can handle both cases:

iteration <- function( dfList, fnct, numberOfIterations, flat=TRUE )
{
  L <- list()

  for (i in 1:numberOfIterations){
    L[[i]] <- lapply( dfList, fnct, i )
    names(L[[i]]) <- paste0( names(dfList), i )
  }
  return( if (flat) unlist(L,recursive=FALSE) else L )
}

Example:

mydflist <- list(
  myfirstdf  = data.frame(matrix(1:20,4,5)),
  myseconddf = data.frame(matrix(1:12,2,6)),
  mythirddf  = data.frame(matrix(1:15,3,5))
)

f <- function(df,i)
{
  longdata <- ncol(df)-i
  sum(df[,1:longdata])
}

results      <- iteration(mydflist,f,4,FALSE)
results_flat <- iteration(mydflist,f,4)

(I've changed the number of iterations from 3 to 4, to avoid confusion with the number of dataframes.) Here is the resulting list results, which is not flat:

> results
[[1]]
[[1]]$myfirstdf1
[1] 136

[[1]]$myseconddf1
[1] 55

[[1]]$mythirddf1
[1] 78


[[2]]
[[2]]$myfirstdf2
[1] 78

[[2]]$myseconddf2
[1] 36

[[2]]$mythirddf2
[1] 45


[[3]]
[[3]]$myfirstdf3
[1] 36

[[3]]$myseconddf3
[1] 21

[[3]]$mythirddf3
[1] 21

[[4]]
[[4]]$myfirstdf4
[1] 10

[[4]]$myseconddf4
[1] 10

[[4]]$mythirddf4
[1] 6

Notice that the number of the iteration step appears twice. For example the result for third dataframe in the first iteration step is

> results[[1]]$mythirddf1
[1] 78

In the names of the flat list results_flat the number of the iteration step appears only once:

> results_flat
$myfirstdf1
[1] 136

$myseconddf1
[1] 55

$mythirddf1
[1] 78

$myfirstdf2
[1] 78

$myseconddf2
[1] 36

$mythirddf2
[1] 45

$myfirstdf3
[1] 36

$myseconddf3
[1] 21

$mythirddf3
[1] 21

$myfirstdf4
[1] 10

$myseconddf4
[1] 10

$mythirddf4
[1] 6

E.g. the result for third dataframe in the first iteration step is

> results_flat$mythirddf1
[1] 78

If you want to access this result via results$mydflist$mythirddf1, then build a one component list results as follows:

> results <- list(mydflist=iteration(mydflist,f,4))

The one and only component of this list results is the list results_flat above, and its name is mydflist:

> results
$mydflist
$mydflist$myfirstdf1
[1] 136

$mydflist$myseconddf1
[1] 55

$mydflist$mythirddf1
[1] 78

$mydflist$myfirstdf2
[1] 78

$mydflist$myseconddf2
[1] 36

$mydflist$mythirddf2
[1] 45

$mydflist$myfirstdf3
[1] 36

$mydflist$myseconddf3
[1] 21

$mydflist$mythirddf3
[1] 21

$mydflist$myfirstdf4
[1] 10

$mydflist$myseconddf4
[1] 10

$mydflist$mythirddf4
[1] 6