diff --git a/R/across.R b/R/across.R
index 4c01413a46..ad9bd54b75 100644
--- a/R/across.R
+++ b/R/across.R
@@ -108,6 +108,17 @@
 #' iris %>%
 #'   mutate(across(where(is.double) & !c(Petal.Length, Petal.Width), round))
 #'
+#' # Using an external vector of names
+#' cols <- c("Sepal.Length", "Petal.Width")
+#' iris %>%
+#'   mutate(across(all_of(cols), round))
+#'
+#' # If the external vector is named, the output columns will be named according
+#' # to those names
+#' names(cols) <- tolower(cols)
+#' iris %>%
+#'   mutate(across(all_of(cols), round))
+#'
 #' # A purrr-style formula
 #' iris %>%
 #'   group_by(Species) %>%
@@ -126,6 +137,12 @@
 #'   group_by(Species) %>%
 #'   summarise(across(starts_with("Sepal"), list(mean = mean, sd = sd), .names = "{.col}.{.fn}"))
 #'
+#' # If a named external vector is used for column selection, .names will use
+#' # those names when constructing the output names
+#' iris %>%
+#'   group_by(Species) %>%
+#'   summarise(across(all_of(cols), mean, .names = "mean_{.col}"))
+#'
 #' # When the list is not named, .fn is replaced by the function's position
 #' iris %>%
 #'   group_by(Species) %>%
diff --git a/man/across.Rd b/man/across.Rd
index a95894fd35..7907d0a9dd 100644
--- a/man/across.Rd
+++ b/man/across.Rd
@@ -152,6 +152,17 @@ iris \%>\%
 iris \%>\%
   mutate(across(where(is.double) & !c(Petal.Length, Petal.Width), round))
 
+# Using an external vector of names
+cols <- c("Sepal.Length", "Petal.Width")
+iris \%>\%
+  mutate(across(all_of(cols), round))
+
+# If the external vector is named, the output columns will be named according
+# to those names
+names(cols) <- tolower(cols)
+iris \%>\%
+  mutate(across(all_of(cols), round))
+
 # A purrr-style formula
 iris \%>\%
   group_by(Species) \%>\%
@@ -170,6 +181,12 @@ iris \%>\%
   group_by(Species) \%>\%
   summarise(across(starts_with("Sepal"), list(mean = mean, sd = sd), .names = "{.col}.{.fn}"))
 
+# If a named external vector is used for column selection, .names will use
+# those names when constructing the output names
+iris \%>\%
+  group_by(Species) \%>\%
+  summarise(across(all_of(cols), mean, .names = "mean_{.col}"))
+
 # When the list is not named, .fn is replaced by the function's position
 iris \%>\%
   group_by(Species) \%>\%