diff --git a/cli/command/completion/functions.go b/cli/command/completion/functions.go
index f461d5befcdc..12e01de08f35 100644
--- a/cli/command/completion/functions.go
+++ b/cli/command/completion/functions.go
@@ -5,7 +5,6 @@ import (
 	"strings"
 
 	"github.com/distribution/reference"
-	"github.com/docker/cli/cli/command/formatter"
 	"github.com/moby/moby/api/types/container"
 	"github.com/moby/moby/client"
 	"github.com/spf13/cobra"
@@ -101,7 +100,13 @@ func ContainerNames(dockerCLI APIClientProvider, all bool, filters ...func(conta
 			if showContainerIDs {
 				names = append(names, ctr.ID)
 			}
-			names = append(names, formatter.StripNamePrefix(ctr.Names)...)
+			for _, n := range ctr.Names {
+				// Skip legacy link names: "/linked-container/link-name"
+				if len(n) <= 1 || strings.IndexByte(n[1:], '/') != -1 {
+					continue
+				}
+				names = append(names, strings.TrimPrefix(n, "/"))
+			}
 		}
 		return names, cobra.ShellCompDirectiveNoFileComp
 	}
diff --git a/cli/command/completion/functions_test.go b/cli/command/completion/functions_test.go
index 27b52cc16bdd..86f10ef950a6 100644
--- a/cli/command/completion/functions_test.go
+++ b/cli/command/completion/functions_test.go
@@ -84,7 +84,7 @@ func TestCompleteContainerNames(t *testing.T) {
 				{ID: "id-b", State: container.StateCreated, Names: []string{"/container-b"}},
 				{ID: "id-a", State: container.StateExited, Names: []string{"/container-a"}},
 			},
-			expOut:       []string{"container-c", "container-c/link-b", "container-b", "container-a"},
+			expOut:       []string{"container-c", "container-b", "container-a"},
 			expOpts:      client.ContainerListOptions{All: true},
 			expDirective: cobra.ShellCompDirectiveNoFileComp,
 		},
@@ -97,7 +97,7 @@ func TestCompleteContainerNames(t *testing.T) {
 				{ID: "id-b", State: container.StateCreated, Names: []string{"/container-b"}},
 				{ID: "id-a", State: container.StateExited, Names: []string{"/container-a"}},
 			},
-			expOut:       []string{"id-c", "container-c", "container-c/link-b", "id-b", "container-b", "id-a", "container-a"},
+			expOut:       []string{"id-c", "container-c", "id-b", "container-b", "id-a", "container-a"},
 			expOpts:      client.ContainerListOptions{All: true},
 			expDirective: cobra.ShellCompDirectiveNoFileComp,
 		},
@@ -107,7 +107,7 @@ func TestCompleteContainerNames(t *testing.T) {
 			containers: []container.Summary{
 				{ID: "id-c", State: container.StateRunning, Names: []string{"/container-c", "/container-c/link-b"}},
 			},
-			expOut:       []string{"container-c", "container-c/link-b"},
+			expOut:       []string{"container-c"},
 			expDirective: cobra.ShellCompDirectiveNoFileComp,
 		},
 		{
@@ -117,7 +117,7 @@ func TestCompleteContainerNames(t *testing.T) {
 				func(ctr container.Summary) bool { return ctr.State == container.StateCreated },
 			},
 			containers: []container.Summary{
-				{ID: "id-c", State: container.StateRunning, Names: []string{"/container-c", "/container-c/link-b"}},
+				{ID: "id-c", State: container.StateRunning, Names: []string{"/container-c"}},
 				{ID: "id-b", State: container.StateCreated, Names: []string{"/container-b"}},
 				{ID: "id-a", State: container.StateExited, Names: []string{"/container-a"}},
 			},
@@ -133,7 +133,7 @@ func TestCompleteContainerNames(t *testing.T) {
 				func(ctr container.Summary) bool { return ctr.State == container.StateCreated },
 			},
 			containers: []container.Summary{
-				{ID: "id-c", State: container.StateRunning, Names: []string{"/container-c", "/container-c/link-b"}},
+				{ID: "id-c", State: container.StateRunning, Names: []string{"/container-c"}},
 				{ID: "id-b", State: container.StateCreated, Names: []string{"/container-b"}},
 				{ID: "id-a", State: container.StateCreated, Names: []string{"/container-a"}},
 			},
diff --git a/cli/command/container/completion.go b/cli/command/container/completion.go
index 73ae61fa1b20..93b9b64433bf 100644
--- a/cli/command/container/completion.go
+++ b/cli/command/container/completion.go
@@ -182,6 +182,35 @@ func completeLink(dockerCLI completion.APIClientProvider) cobra.CompletionFunc {
 	}
 }
 
+// completeLinks implements shell completion for the `--link` option  of `rm --link`.
+//
+// It contacts the API to get names of legacy links on containers.
+// In case of an error, an empty list is returned.
+func completeLinks(dockerCLI completion.APIClientProvider) cobra.CompletionFunc {
+	return func(cmd *cobra.Command, args []string, toComplete string) ([]string, cobra.ShellCompDirective) {
+		res, err := dockerCLI.Client().ContainerList(cmd.Context(), client.ContainerListOptions{
+			All: true,
+		})
+		if err != nil {
+			return nil, cobra.ShellCompDirectiveError
+		}
+		var names []string
+		for _, ctr := range res.Items {
+			if len(ctr.Names) <= 1 {
+				// Container has no links names.
+				continue
+			}
+			for _, n := range ctr.Names {
+				// Skip legacy link names: "/linked-container/link-name"
+				if len(n) > 1 && strings.IndexByte(n[1:], '/') != -1 {
+					names = append(names, strings.TrimPrefix(n, "/"))
+				}
+			}
+		}
+		return names, cobra.ShellCompDirectiveNoFileComp
+	}
+}
+
 // completeLogDriver implements shell completion for the `--log-driver` option  of `run` and `create`.
 // The log drivers are collected from a call to the Info endpoint with a fallback to a hard-coded list
 // of the build-in log drivers.
diff --git a/cli/command/container/completion_test.go b/cli/command/container/completion_test.go
index 21b20211d232..649e4701e890 100644
--- a/cli/command/container/completion_test.go
+++ b/cli/command/container/completion_test.go
@@ -135,3 +135,44 @@ func TestCompleteSignals(t *testing.T) {
 	assert.Check(t, len(values) > 1)
 	assert.Check(t, is.Len(values, len(signal.SignalMap)))
 }
+
+func TestCompleteLinks(t *testing.T) {
+	tests := []struct {
+		doc              string
+		showAll, showIDs bool
+		filters          []func(container.Summary) bool
+		containers       []container.Summary
+		expOut           []string
+		expDirective     cobra.ShellCompDirective
+	}{
+		{
+			doc:          "no results",
+			expDirective: cobra.ShellCompDirectiveNoFileComp,
+		},
+		{
+			doc:     "all containers",
+			showAll: true,
+			containers: []container.Summary{
+				{ID: "id-c", State: container.StateRunning, Names: []string{"/container-c", "/container-c/link-b", "/container-c/link-c"}},
+				{ID: "id-b", State: container.StateCreated, Names: []string{"/container-b", "/container-b/link-a"}},
+				{ID: "id-a", State: container.StateExited, Names: []string{"/container-a"}},
+			},
+			expOut:       []string{"container-c/link-b", "container-c/link-c", "container-b/link-a"},
+			expDirective: cobra.ShellCompDirectiveNoFileComp,
+		},
+	}
+
+	for _, tc := range tests {
+		t.Run(tc.doc, func(t *testing.T) {
+			comp := completeLinks(test.NewFakeCli(&fakeClient{
+				containerListFunc: func(client.ContainerListOptions) (client.ContainerListResult, error) {
+					return client.ContainerListResult{Items: tc.containers}, nil
+				},
+			}))
+
+			containers, directives := comp(&cobra.Command{}, nil, "")
+			assert.Check(t, is.Equal(directives&tc.expDirective, tc.expDirective))
+			assert.Check(t, is.DeepEqual(containers, tc.expOut))
+		})
+	}
+}
diff --git a/cli/command/container/rm.go b/cli/command/container/rm.go
index 8251f2a9dd70..c38256a468b4 100644
--- a/cli/command/container/rm.go
+++ b/cli/command/container/rm.go
@@ -27,6 +27,11 @@ type rmOptions struct {
 func newRmCommand(dockerCLI command.Cli) *cobra.Command {
 	var opts rmOptions
 
+	completeLinkNames := completeLinks(dockerCLI)
+	completeNames := completion.ContainerNames(dockerCLI, true, func(ctr container.Summary) bool {
+		return opts.force || ctr.State == container.StateExited || ctr.State == container.StateCreated
+	})
+
 	cmd := &cobra.Command{
 		Use:   "rm [OPTIONS] CONTAINER [CONTAINER...]",
 		Short: "Remove one or more containers",
@@ -38,9 +43,13 @@ func newRmCommand(dockerCLI command.Cli) *cobra.Command {
 		Annotations: map[string]string{
 			"aliases": "docker container rm, docker container remove, docker rm",
 		},
-		ValidArgsFunction: completion.ContainerNames(dockerCLI, true, func(ctr container.Summary) bool {
-			return opts.force || ctr.State == container.StateExited || ctr.State == container.StateCreated
-		}),
+		ValidArgsFunction: func(cmd *cobra.Command, args []string, toComplete string) ([]string, cobra.ShellCompDirective) {
+			if opts.rmLink {
+				// "--link" (remove link) is set; provide link names instead of container (primary) names.
+				return completeLinkNames(cmd, args, toComplete)
+			}
+			return completeNames(cmd, args, toComplete)
+		},
 		DisableFlagsInUseLine: true,
 	}