diff --git a/staging/src/k8s.io/dynamic-resource-allocation/controller/controller.go b/staging/src/k8s.io/dynamic-resource-allocation/controller/controller.go
index a10609daef9..842e53f75ae 100644
--- a/staging/src/k8s.io/dynamic-resource-allocation/controller/controller.go
+++ b/staging/src/k8s.io/dynamic-resource-allocation/controller/controller.go
@@ -162,6 +162,7 @@ type controller struct {
 	driver              Driver
 	setReservedFor      bool
 	kubeClient          kubernetes.Interface
+	claimNameLookup     *resourceclaim.Lookup
 	queue               workqueue.RateLimitingInterface
 	eventRecorder       record.EventRecorder
 	rcLister            resourcev1alpha2listers.ResourceClassLister
@@ -186,6 +187,7 @@ func New(
 	rcInformer := informerFactory.Resource().V1alpha2().ResourceClasses()
 	claimInformer := informerFactory.Resource().V1alpha2().ResourceClaims()
 	schedulingCtxInformer := informerFactory.Resource().V1alpha2().PodSchedulingContexts()
+	claimNameLookup := resourceclaim.NewNameLookup(kubeClient)
 
 	eventBroadcaster := record.NewBroadcaster()
 	go func() {
@@ -224,6 +226,7 @@ func New(
 		driver:              driver,
 		setReservedFor:      true,
 		kubeClient:          kubeClient,
+		claimNameLookup:     claimNameLookup,
 		rcLister:            rcInformer.Lister(),
 		rcSynced:            rcInformer.Informer().HasSynced,
 		claimCache:          claimCache,
@@ -651,7 +654,7 @@ func (ctrl *controller) allocateClaims(ctx context.Context, claims []*ClaimAlloc
 }
 
 func (ctrl *controller) checkPodClaim(ctx context.Context, pod *v1.Pod, podClaim v1.PodResourceClaim) (*ClaimAllocation, error) {
-	claimName, mustCheckOwner, err := resourceclaim.Name(pod, &podClaim)
+	claimName, mustCheckOwner, err := ctrl.claimNameLookup.Name(pod, &podClaim)
 	if err != nil {
 		return nil, err
 	}
diff --git a/staging/src/k8s.io/dynamic-resource-allocation/go.mod b/staging/src/k8s.io/dynamic-resource-allocation/go.mod
index 82452ecc413..3ca9d319bdc 100644
--- a/staging/src/k8s.io/dynamic-resource-allocation/go.mod
+++ b/staging/src/k8s.io/dynamic-resource-allocation/go.mod
@@ -14,6 +14,7 @@ require (
 	k8s.io/client-go v0.0.0
 	k8s.io/klog/v2 v2.100.1
 	k8s.io/kubelet v0.0.0
+	k8s.io/utils v0.0.0-20230726121419-3b25d923346b
 )
 
 require (
@@ -50,7 +51,6 @@ require (
 	gopkg.in/yaml.v2 v2.4.0 // indirect
 	gopkg.in/yaml.v3 v3.0.1 // indirect
 	k8s.io/kube-openapi v0.0.0-20230905202853-d090da108d2f // indirect
-	k8s.io/utils v0.0.0-20230726121419-3b25d923346b // indirect
 	sigs.k8s.io/json v0.0.0-20221116044647-bc3834ca7abd // indirect
 	sigs.k8s.io/structured-merge-diff/v4 v4.3.0 // indirect
 	sigs.k8s.io/yaml v1.3.0 // indirect
diff --git a/staging/src/k8s.io/dynamic-resource-allocation/resourceclaim/resourceclaim.go b/staging/src/k8s.io/dynamic-resource-allocation/resourceclaim/resourceclaim.go
index 3fb1bced3d6..93d69695ef4 100644
--- a/staging/src/k8s.io/dynamic-resource-allocation/resourceclaim/resourceclaim.go
+++ b/staging/src/k8s.io/dynamic-resource-allocation/resourceclaim/resourceclaim.go
@@ -26,10 +26,14 @@ package resourceclaim
 import (
 	"errors"
 	"fmt"
+	"os"
+	"strings"
 
 	v1 "k8s.io/api/core/v1"
 	resourcev1alpha2 "k8s.io/api/resource/v1alpha2"
 	metav1 "k8s.io/apimachinery/pkg/apis/meta/v1"
+	"k8s.io/client-go/kubernetes"
+	"k8s.io/utils/ptr"
 )
 
 var (
@@ -59,9 +63,7 @@ var (
 //     In this case the boolean determines whether IsForPod must be called
 //     after retrieving the ResourceClaim and before using it.
 //
-// If podClaim.Template is not nil, the caller must check that the
-// ResourceClaim is indeed the one that was created for the Pod by calling
-// IsUsable.
+// Determining the name depends on Kubernetes >= 1.28.
 func Name(pod *v1.Pod, podClaim *v1.PodResourceClaim) (name *string, mustCheckOwner bool, err error) {
 	switch {
 	case podClaim.Source.ResourceClaimName != nil:
@@ -78,6 +80,73 @@ func Name(pod *v1.Pod, podClaim *v1.PodResourceClaim) (name *string, mustCheckOw
 	}
 }
 
+// NewNameLookup returns an object which handles determining the name of
+// a ResourceClaim. In contrast to the stand-alone Name it is compatible
+// also with Kubernetes < 1.28.
+//
+// Providing a client is optional. If none is available, then code can pass nil
+// and users can set the DRA_WITH_DETERMINISTIC_RESOURCE_CLAIM_NAMES env
+// variable to an arbitrary non-empty value to use the naming from Kubernetes <
+// 1.28.
+func NewNameLookup(client kubernetes.Interface) *Lookup {
+	return &Lookup{client: client}
+}
+
+// Lookup stores the state which is necessary to look up ResourceClaim names.
+type Lookup struct {
+	client       kubernetes.Interface
+	usePodStatus *bool
+}
+
+// Name is a variant of the stand-alone Name with support also for Kubernetes < 1.28.
+func (l *Lookup) Name(pod *v1.Pod, podClaim *v1.PodResourceClaim) (name *string, mustCheckOwner bool, err error) {
+	if l.usePodStatus == nil {
+		if value, _ := os.LookupEnv("DRA_WITH_DETERMINISTIC_RESOURCE_CLAIM_NAMES"); value != "" {
+			l.usePodStatus = ptr.To(false)
+		} else if l.client != nil {
+			// Check once. This does not detect upgrades or
+			// downgrades, but that is good enough for the simple
+			// test scenarios that the Kubernetes < 1.28 support is
+			// meant for.
+			info, err := l.client.Discovery().ServerVersion()
+			if err != nil {
+				return nil, false, fmt.Errorf("look up server version: %v", err)
+			}
+			if info.Major == "" {
+				// Fake client...
+				l.usePodStatus = ptr.To(true)
+			} else {
+				switch strings.Compare(info.Major, "1") {
+				case -1:
+					// Huh?
+					l.usePodStatus = ptr.To(false)
+				case 0:
+					// info.Minor may have a suffix which makes it larger than 28.
+					// We don't care about pre-releases here.
+					l.usePodStatus = ptr.To(strings.Compare("28", info.Minor) <= 0)
+				case 1:
+					// Kubernetes 2? Yeah!
+					l.usePodStatus = ptr.To(true)
+				}
+			}
+		}
+	}
+
+	if *l.usePodStatus {
+		return Name(pod, podClaim)
+	}
+
+	switch {
+	case podClaim.Source.ResourceClaimName != nil:
+		return podClaim.Source.ResourceClaimName, false, nil
+	case podClaim.Source.ResourceClaimTemplateName != nil:
+		name := pod.Name + "-" + podClaim.Name
+		return &name, true, nil
+	default:
+		return nil, false, fmt.Errorf(`pod "%s/%s", spec.resourceClaim %q: %w`, pod.Namespace, pod.Name, podClaim.Name, ErrAPIUnsupported)
+	}
+}
+
 // IsForPod checks that the ResourceClaim is the one that
 // was created for the Pod. It returns an error that is informative
 // enough to be returned by the caller without adding further details