diff --git a/pkg/sentry/control/proc.go b/pkg/sentry/control/proc.go
index 7fd4ffaf0..fbc025233 100644
--- a/pkg/sentry/control/proc.go
+++ b/pkg/sentry/control/proc.go
@@ -266,9 +266,8 @@ func (proc *Proc) execAsync(args *ExecArgs) (*kernel.ThreadGroup, kernel.ThreadI
 		initArgs.Filename = resolved
 	}
 
-	// TODO(gvisor.dev/issue/1956): Container name is not really needed because
-	// exec processes are not restored, but add it for completeness.
-	ttyFile, err := fdimport.Import(ctx, fdTable, args.StdioIsPty, args.KUID, args.KGID, fdMap, "")
+	containerName := proc.Kernel.ContainerNameGivenID(args.ContainerID)
+	ttyFile, err := fdimport.Import(ctx, fdTable, args.StdioIsPty, args.KUID, args.KGID, fdMap, containerName)
 	if err != nil {
 		return nil, 0, nil, err
 	}
diff --git a/pkg/sentry/kernel/kernel.go b/pkg/sentry/kernel/kernel.go
index 73237adb7..6aa6a21f6 100644
--- a/pkg/sentry/kernel/kernel.go
+++ b/pkg/sentry/kernel/kernel.go
@@ -348,6 +348,9 @@ type Kernel struct {
 	// devGofers maps container ID to its device gofer client.
 	devGofers   map[string]*devutil.GoferClient `state:"nosave"`
 	devGofersMu sync.Mutex                      `state:"nosave"`
+
+	// cid -> name.
+	containerNames map[string]string
 }
 
 // InitKernelArgs holds arguments to Init.
@@ -454,6 +457,7 @@ func (k *Kernel) Init(args InitKernelArgs) error {
 		args.MaxFDLimit = MaxFdLimit
 	}
 	k.MaxFDLimit.Store(args.MaxFDLimit)
+	k.containerNames = make(map[string]string)
 
 	ctx := k.SupervisorContext()
 	if err := k.vfs.Init(ctx); err != nil {
@@ -1956,3 +1960,13 @@ func (k *Kernel) cleaupDevGofers() {
 	}
 	k.devGofers = nil
 }
+
+// RegisterContainerName registers a container name for a given container ID.
+func (k *Kernel) RegisterContainerName(cid, containerName string) {
+	k.containerNames[cid] = containerName
+}
+
+// ContainerNameGivenID returns the container name for a given container ID.
+func (k *Kernel) ContainerNameGivenID(cid string) string {
+	return k.containerNames[cid]
+}
diff --git a/runsc/boot/loader.go b/runsc/boot/loader.go
index a9c214e41..3edbcb157 100644
--- a/runsc/boot/loader.go
+++ b/runsc/boot/loader.go
@@ -543,6 +543,7 @@ func New(args Args) (*Loader, error) {
 		}
 	}
 
+	k.RegisterContainerName(args.ID, info.containerName)
 	eid := execID{cid: args.ID}
 	l := &Loader{
 		k:             k,
@@ -954,6 +955,7 @@ func (l *Loader) startSubcontainer(spec *specs.Spec, conf *config.Config, cid st
 		})
 	}
 
+	l.k.RegisterContainerName(cid, info.containerName)
 	l.k.StartProcess(ep.tg)
 	// No more failures from this point on.
 	cu.Release()