What happened:

Names allowed for Pods, Deployment, StatefulSet follow DNS subdomain name defined in RFC 1123.
Pods controlled by Deployment follows DNS subdomain name standard as well.

However, Pod controlled by StatefuSet is following DNS label standard.
StatefulSet allows names with "." , but Pods created by the StatefulSet fails with error --

Events:
  Type     Reason        Age                     From                    Message
  ----     ------        ----                    ----                    -------
  Warning  FailedCreate  4m23s (x17 over 9m51s)  statefulset-controller  create Pod sts1-vol.1-0 in StatefulSet sts1-vol.1 failed error: Pod "sts1-vol.1-0" is invalid: spec.hostname: Invalid value: "sts1-vol.1-0": a DNS-1123 label must consist of lower case alphanumeric characters or '-', and must start and end with an alphanumeric character (e.g. 'my-name',  or '123-abc', regex used for validation is '[a-z0-9]([-a-z0-9]*[a-z0-9])?')

What you expected to happen:

Since "." character is allowed in the StatefulSet name, Pod replicas controlled by the StatefulSet should allow "." character as well.
If "." is not possible for Pods controlled by StatefulSet, then StatefulSet creation should fail for "." character in the name.

How to reproduce it (as minimally and precisely as possible):

$ kubectl create -f 1sts-1vol-dot.yaml -n test
persistentvolumeclaim/pvc-3 created
statefulset.apps/sts1-vol.1 created

YAML FILE -->

apiVersion: v1
kind: PersistentVolumeClaim
metadata:
  name: pvc-3
spec:
  accessModes:
    - ReadWriteMany
  resources:
    requests:
      storage: 5Gi
  storageClassName: rook-cephfs
---
apiVersion: apps/v1
kind: StatefulSet
metadata:
  name: sts1-vol.1
spec:
  replicas: 2
  selector:
    matchLabels:
      app: ubuntu-ss
  serviceName: ubuntu-svc
  template:
    metadata:
      labels:
        app: ubuntu-ss
    spec:
      containers:
      - name: ubuntu
        image: ubuntu
        ports:
        - containerPort: 80
          name: web
        volumeMounts:
          - name: data
            mountPath: /mnt/data
        command: ["/bin/sh", "-c"]
        args:
          - while true; do
              sleep 3600;
              done
      volumes:
      - name: data
        persistentVolumeClaim:
          claimName: pvc-3
          readOnly: false

Anything else we need to know?:

Pods controlled by ReplicaSet gets successfully created as it follows DNS subdomain standard.

Environment:

• Kubernetes version (use kubectl version):

Client Version: version.Info{Major:"1", Minor:"21", GitVersion:"v1.21.2", GitCommit:"092fbfbf53427de67cac1e9fa54aaa09a28371d7", GitTreeState:"clean", BuildDate:"2021-06-16T12:59:11Z", GoVersion:"go1.16.5", Compiler:"gc", Platform:"linux/amd64"}
Server Version: version.Info{Major:"1", Minor:"19", GitVersion:"v1.19.11", GitCommit:"c6a2f08fc4378c5381dd948d9ad9d1080e3e6b33", GitTreeState:"clean", BuildDate:"2021-05-12T12:19:22Z", GoVersion:"go1.15.12", Compiler:"gc", Platform:"linux/amd64"}

• Cloud provider or hardware configuration:

Bare Metal

• OS (e.g: cat /etc/os-release):

NAME="CentOS Linux"
VERSION="8"
ID="centos"
ID_LIKE="rhel fedora"
VERSION_ID="8"
PLATFORM_ID="platform:el8"
PRETTY_NAME="CentOS Linux 8"
ANSI_COLOR="0;31"
CPE_NAME="cpe:/o:centos:centos:8"
HOME_URL="https://centos.org/"
BUG_REPORT_URL="https://bugs.centos.org/"
CENTOS_MANTISBT_PROJECT="CentOS-8"
CENTOS_MANTISBT_PROJECT_VERSION="8"

• Kernel (e.g. uname -a):

Linux 'redacted hostname' 4.18.0-240.el8.x86_64 #1 SMP Fri Sep 25 19:48:47 UTC 2020 x86_64 x86_64 x86_64 GNU/Linux

• Install tools:

kubeadm version: &version.Info{Major:"1", Minor:"19+", GitVersion:"v1.19.8-eks-1-19-4", GitCommit:"832dfd094a0c1a0dfe4303775e5e6047473bef6a", GitTreeState:"clean", BuildDate:"2021-05-05T18:01:29Z", GoVersion:"go1.15.11", Compiler:"gc", Platform:"linux/amd64"}

• Network plugin and version (if this is a network-related bug):

Flannel

/sig api-machinery