diff --git a/R/PipeOpRenameColumns.R b/R/PipeOpRenameColumns.R
index b7d175e56..a96cf02c1 100644
--- a/R/PipeOpRenameColumns.R
+++ b/R/PipeOpRenameColumns.R
@@ -28,17 +28,21 @@
 #'
 #' @section Parameters:
 #' The parameters are the parameters inherited from [`PipeOpTaskPreproc`], as well as:
-#' * `renaming` :: named `character`\cr
-#'   Named `character` vector. The names of the vector specify the old column names that should be
-#'   changed to the new column names as given by the elements of the vector. Initialized to the empty
-#'   character vector.
+#' * `renaming` :: named `character` | `function`\cr
+#'   Takes the form of either a named `character` or a `function`.
+#'   For a named `character` vector the names of the vector elements specify the
+#'   old column names and the corresponding element values give the new column names.
+#'   Initialized to an empty character vector.
+#'   A `function` specifies how the old column names should be changed to the new column names.
+#'   The function must return a `character` vector with one entry per input column name so that each selected column receives a new name.
+#'   To choose columns use the `affect_columns` parameter. No function is initialized.
 #' * `ignore_missing` :: `logical(1)`\cr
 #'   Ignore if columns named in `renaming` are not found in the input [`Task`][mlr3::Task]. If this is
 #'   `FALSE`, then names found in `renaming` not found in the [`Task`][mlr3::Task] cause an error.
 #'   Initialized to `FALSE`.
 #'
 #' @section Internals:
-#' Uses the `$rename()` mutator of the [`Task`][mlr3::Task] to set the new column names.
+#' Uses the `$rename()` mutator of the [`Task`][mlr3::Task] to set new column names.
 #'
 #' @section Fields:
 #' Only fields inherited from [`PipeOp`].
@@ -56,36 +60,53 @@
 #' task = tsk("iris")
 #' pop = po("renamecolumns", param_vals = list(renaming = c("Petal.Length" = "PL")))
 #' pop$train(list(task))
+#'
+#' pof = po("renamecolumns",
+#'          param_vals = list(renaming = function(colnames) {sub("Petal", "P", colnames)}))
+#' pof$train(list(task))
+#'
+
 PipeOpRenameColumns = R6Class("PipeOpRenameColumns",
   inherit = PipeOpTaskPreprocSimple,
   public = list(
     initialize = function(id = "renamecolumns", param_vals = list()) {
       ps = ps(
         renaming = p_uty(
-          custom_check = crate(function(x) check_character(x, any.missing = FALSE, names = "strict") %check&&% check_names(x, type = "strict"),
-                               .parent = topenv()),
+          custom_check = crate(function(x) (check_character(x, any.missing = FALSE, names = "strict") %check&&% check_names(x, type = "strict")) %check||% check_function(x)),
           tags = c("train", "predict", "required")
         ),
         ignore_missing = p_lgl(tags = c("train", "predict", "required"))
       )
       ps$values = list(renaming = character(0), ignore_missing = FALSE)
-      super$initialize(id, ps, param_vals = param_vals, can_subset_cols = FALSE)
+      super$initialize(id, ps, param_vals = param_vals, can_subset_cols = TRUE)
     }
   ),
   private = list(
+    .get_state = function(task) {
+      if (is.function(self$param_set$values$renaming)) {
+        new_names = self$param_set$values$renaming(task$feature_names)
+        assert_character(new_names, any.missing = FALSE, len = length(task$feature_names), .var.name = "the value returned by `renaming` function")
+        names(new_names) = task$feature_names
+        list(old_names = task$feature_names, new_names = new_names)
+      } else {
+        pv = self$param_set$get_values(tags = "train")
+        new_names = pv$renaming
+        innames = names(new_names)
+        nontargets = task$col_roles
+        nontargets$target = NULL
+        takenames = innames %in% unlist(nontargets)
+        if (!pv$ignore_missing && !all(takenames)) {
+          # we can't rely on task$rename because it could also change the target name, which we don't want.
+          stopf("The names %s from `renaming` parameter were not found in the Task.", str_collapse(innames[!takenames]))
+        }
+        list(old_names = innames[takenames], new_names = new_names[takenames])
+      }
+    },
     .transform = function(task) {
-      if (!length(self$param_set$values$renaming)) {
+      if (!length(self$state$new_names)) {
         return(task)  # early exit
       }
-      innames = names(self$param_set$values$renaming)
-      nontargets = task$col_roles
-      nontargets$target = NULL
-      takenames = innames %in% unlist(nontargets)
-      if (!self$param_set$values$ignore_missing && !all(takenames)) {
-        # we can't rely on task$rename because it could also change the target name, which we don't want.
-        stopf("The names %s from `renaming` parameter were not found in the Task.", str_collapse(innames[!takenames]))
-      }
-      task$rename(old = innames[takenames], new = self$param_set$values$renaming[takenames])
+      task$rename(old = self$state$old_names, new = self$state$new_names)
     }
   )
 )
diff --git a/man/mlr_pipeops_renamecolumns.Rd b/man/mlr_pipeops_renamecolumns.Rd
index 131433937..1eebf6f2f 100644
--- a/man/mlr_pipeops_renamecolumns.Rd
+++ b/man/mlr_pipeops_renamecolumns.Rd
@@ -40,10 +40,14 @@ The \verb{$state} is a named \code{list} with the \verb{$state} elements inherit
 
 The parameters are the parameters inherited from \code{\link{PipeOpTaskPreproc}}, as well as:
 \itemize{
-\item \code{renaming} :: named \code{character}\cr
-Named \code{character} vector. The names of the vector specify the old column names that should be
-changed to the new column names as given by the elements of the vector. Initialized to the empty
-character vector.
+\item \code{renaming} :: named \code{character} | \code{function}\cr
+Takes the form of either a named \code{character} or a \code{function}.
+For a named \code{character} vector the names of the vector elements specify the
+old column names and the corresponding element values give the new column names.
+Initialized to an empty character vector.
+A \code{function} specifies how the old column names should be changed to the new column names.
+The function must return a \code{character} vector with one entry per input column name so that each selected column receives a new name.
+To choose columns use the \code{affect_columns} parameter. No function is initialized.
 \item \code{ignore_missing} :: \code{logical(1)}\cr
 Ignore if columns named in \code{renaming} are not found in the input \code{\link[mlr3:Task]{Task}}. If this is
 \code{FALSE}, then names found in \code{renaming} not found in the \code{\link[mlr3:Task]{Task}} cause an error.
@@ -53,7 +57,7 @@ Initialized to \code{FALSE}.
 
 \section{Internals}{
 
-Uses the \verb{$rename()} mutator of the \code{\link[mlr3:Task]{Task}} to set the new column names.
+Uses the \verb{$rename()} mutator of the \code{\link[mlr3:Task]{Task}} to set new column names.
 }
 
 \section{Fields}{
@@ -72,6 +76,11 @@ library("mlr3")
 task = tsk("iris")
 pop = po("renamecolumns", param_vals = list(renaming = c("Petal.Length" = "PL")))
 pop$train(list(task))
+
+pof = po("renamecolumns",
+         param_vals = list(renaming = function(colnames) {sub("Petal", "P", colnames)}))
+pof$train(list(task))
+
 }
 \seealso{
 https://mlr-org.com/pipeops.html
diff --git a/tests/testthat/test_pipeop_renamecolumns.R b/tests/testthat/test_pipeop_renamecolumns.R
index 2439a1d11..536f44687 100644
--- a/tests/testthat/test_pipeop_renamecolumns.R
+++ b/tests/testthat/test_pipeop_renamecolumns.R
@@ -39,3 +39,15 @@ test_that("error handling", {
   op$param_set$values$ignore_missing = TRUE
   expect_equal(task$data(), op$train(list(task))[[1]]$data())
 })
+
+test_that("assert on function works", {
+  task = mlr_tasks$get("iris")
+  expect_error(po("renamecolumns", param_vals = list(renaming = 1 + 1)))
+})
+
+test_that("assert on function works", {
+  task = mlr_tasks$get("iris")
+  po = po("renamecolumns", param_vals = list(renaming = function(colnames) sub("Petal", "P", colnames)))
+  result = po$train(list(task))
+  expect_equal(result[[1]]$feature_names, c("P.Length", "P.Width", "Sepal.Length", "Sepal.Width"))
+})