It could be done the following way:

    persVolC := client.CoreV1().PersistentVolumeClaims("default")

    data := `
    [
      { "op": "add", "path": "/metadata/labels/mylabel", "value": "myvalue" }
    ]
    `
    updatedPvc, err := persVolC.Patch(ctx, "name-of-pvc", types.JSONPatchType, []byte(data), meta_v1.PatchOptions{})
    if err != nil {
        log.Fatal(err)
    }

Full example at go playground.

And here you can read about JSON patch standard.

This is an example in which we're going to iterate over the List of PersistentVolumeClaims in the default namespace, and we're going to set an specific label my_label: label_test to all of those Items. You can get an specific PVC instead of List all with the func Get(ctx context.Context, name string, opts metav1.GetOptions)

package main

import (
    "context"
    "fmt"
    "log"

    meta_v1 "k8s.io/apimachinery/pkg/apis/meta/v1"
    "k8s.io/client-go/kubernetes"
    "k8s.io/client-go/tools/clientcmd"
)

func newClient(contextName string) (kubernetes.Interface, error) {
    configOverrides := &clientcmd.ConfigOverrides{CurrentContext: contextName}

    loadingRules := clientcmd.NewDefaultClientConfigLoadingRules()
    config, err := clientcmd.NewNonInteractiveDeferredLoadingClientConfig(loadingRules, configOverrides).ClientConfig()
    if err != nil {
        return nil, err
    }

    return kubernetes.NewForConfig(config)
}

func main() {
    ctx, cancel := context.WithCancel(context.Background())
    defer cancel()

    client, err := newClient("")
    if err != nil {
        log.Fatal(err)
    }

    label := make(map[string]string)
    label["my_label"] = "label_test"
    persVolC := client.CoreV1().PersistentVolumeClaims("default")

    pvcs, err := persVolC.List(ctx, meta_v1.ListOptions{})
    for _, pvc := range pvcs.Items {
        vol := pvc.DeepCopy()
        vol.ObjectMeta.Labels = label
        upd, err := persVolC.Update(ctx, vol, meta_v1.UpdateOptions{})
        if err != nil {
            log.Fatal(err)
        }
        fmt.Println(upd)
    }
}

If you want to check if a label exist and update it, you can replace vol.ObjectMeta.Labels = label by

if _, ok := vol.ObjectMeta.Labels["my_label"]; ok {
    vol.ObjectMeta.Labels["my_label"] = "my_new_label"
}