Update I suspect this to be a google issue, I have created a new more clean question here.

Update: yes this is different than the suggested "This question may already have an answer here:", as this is about a "Service Account" - not a "User accounts".

Do you now how to use a private registry like Google Container Registry from DigitalOcean or any other Kubernetes not running on the same provider?

I tried following this, but unfortunately it did not work for me.

Update: I suspect it to be a Google SA issue, I will go and try using Docker Hub and get back if that succeeds. I am still curious to see the solution for this, so please let me know - thanks!
Update: Also tried this Update: tried to activate Google Service Account
Update: tried to download Google Service Account key
Update: in the linked description is says:

kubectl create secret docker-registry $SECRETNAME \
  --docker-server=https://gcr.io \
  --docker-username=_json_key \
  --docker-email=user@example.com \
  --docker-password="$(cat k8s-gcr-auth-ro.json)"

Is the --docker-password="$(cat k8s-gcr-auth-ro.json)" really the password?

If I do cat k8s-gcr-auth-ro.json the format is:

{
  "type": "service_account",
  "project_id": "<xxx>",
  "private_key_id": "<xxx>",
  "private_key": "-----BEGIN PRIVATE KEY-----\<xxx>\n-----END PRIVATE KEY-----\n",
  "client_email": "k8s-gcr-auth-ro@<xxx>.iam.gserviceaccount.com",
  "client_id": "<xxx>",
  "auth_uri": "https://accounts.google.com/o/oauth2/auth",
  "token_uri": "https://oauth2.googleapis.com/token",
  "auth_provider_x509_cert_url": "https://www.googleapis.com/oauth2/v1/certs",
  "client_x509_cert_url": "https://www.googleapis.com/robot/v1/metadata/x509/k8s-gcr-auth-ro%<xxx>.iam.gserviceaccount.com"
}

kubectl get pods I get: ...is waiting to start: image can't be pulled

from a deployment with:

image: gcr.io/<project name>/<image name>:v1

deployment.yaml

# K8s - Deployment
apiVersion: extensions/v1beta1
kind: Deployment
metadata:
  name: <image-name>-deployment-v1
spec:
  replicas: 1
  template:
    metadata:
      labels:
        app: <image-name>-deployment
        version: v1
    spec:
      containers:
      - name: <image-name>
        image: gcr.io/<project-name>/<image-name>:v1
        imagePullPolicy: Always
        ports:
        - containerPort: 80
      imagePullSecrets:
        - name: <name-of-secret>

I can see from the following that it logs: repository does not exist or may require 'docker login'

kubectl describe pod :

k describe pod <image-name>-deployment-v1-844568c768-5b2rt

Name:               <image-name>-deployment-v1-844568c768-5b2rt
Namespace:          default
Priority:           0
PriorityClassName:  <none>
Node:               my-cluster-digitalocean-1-7781/10.135.153.236
Start Time:         Mon, 25 Mar 2019 15:51:37 +0100
Labels:             app=<image-name>-deployment
                    pod-template-hash=844568c768
                    version=v1
Annotations:        <none>
Status:             Pending
IP:                 <ip address>
Controlled By:      ReplicaSet/<image-name>-deployment-v1-844568c768
Containers:
  chat-server:
    Container ID:   
    Image:          gcr.io/<project-name/<image-name>:v1
    Image ID:       
    Port:           80/TCP
    Host Port:      0/TCP
    State:          Waiting
      Reason:       ImagePullBackOff
    Ready:          False
    Restart Count:  0
    Environment:    <none>
    Mounts:
      /var/run/secrets/kubernetes.io/serviceaccount from default-token-dh8dh (ro)
Conditions:
  Type              Status
  Initialized       True 
  Ready             False 
  ContainersReady   False 
  PodScheduled      True 
Volumes:
  default-token-dh8dh:
    Type:        Secret (a volume populated by a Secret)
    SecretName:  default-token-dh8dh
    Optional:    false
QoS Class:       BestEffort
Node-Selectors:  <none>
Tolerations:     node.kubernetes.io/not-ready:NoExecute for 300s
                 node.kubernetes.io/unreachable:NoExecute for 300s
Events:
  Type     Reason          Age                From                                        Message
  ----     ------          ----               ----                                        -------
  Normal   Scheduled       50s                default-scheduler                           Successfully assigned default/<image-name>-deployment-v1-844568c768-5b2rt to my-cluster-digitalocean-1-7781
  Normal   Pulling         37s (x2 over 48s)  kubelet, my-cluster-digitalocean-1-7781  pulling image "gcr.io/<project-name><image-name>:v1"
  Warning  Failed          37s (x2 over 48s)  kubelet, my-cluster-digitalocean-1-7781  Failed to pull image "gcr.io/<project-name>/<image-name>:v1": rpc error: code = Unknown desc = Error response from daemon: pull access denied for gcr.io/<project-name>/<image-name>, repository does not exist or may require 'docker login'
  Warning  Failed          37s (x2 over 48s)  kubelet, my-cluster-digitalocean-1-7781  Error: ErrImagePull
  Normal   SandboxChanged  31s (x7 over 47s)  kubelet, my-cluster-digitalocean-1-7781  Pod sandbox changed, it will be killed and re-created.
  Normal   BackOff         29s (x6 over 45s)  kubelet, my-cluster-digitalocean-1-7781  Back-off pulling image "gcr.io/<project-name>/<image-name>:v1"
  Warning  Failed          29s (x6 over 45s)  kubelet, my-cluster-digitalocean-1-7781  Error: ImagePullBackOff

Just a note: docker pull on local machine pulls the image alright