When a (recommended/conditional) release image is provided with --to-image='', the specified image name is not preserved in the ClusterVersion object.

100% with oc >4.9

$ oc version
Client Version: 4.12.2
Kustomize Version: v4.5.7
Server Version: 4.12.2
Kubernetes Version: v1.25.4+a34b9e9

$ oc get clusterversion/version -o jsonpath='{.status.desired}'|jq
{
  "channels": [
    "candidate-4.12",
    "candidate-4.13",
    "eus-4.12",
    "fast-4.12",
    "stable-4.12"
  ],
  "image": "quay.io/openshift-release-dev/ocp-release@sha256:31c7741fc7bb73ff752ba43f5acf014b8fadd69196fc522241302de918066cb1",
  "url": "https://access.redhat.com/errata/RHSA-2023:0569",
  "version": "4.12.2"
}
$ oc adm release info 4.12.3 -o jsonpath='{.image}'
quay.io/openshift-release-dev/ocp-release@sha256:382f271581b9b907484d552bd145e9a5678e9366330059d31b007f4445d99e36
$ skopeo copy docker://quay.io/openshift-release-dev/ocp-release@sha256:382f271581b9b907484d552bd145e9a5678e9366330059d31b007f4445d99e36 docker://quay.example.com/playground/release-images
Getting image source signatures
Copying blob 64096b96a7b0 done  
Copying blob 0e0550faf8e0 done  
Copying blob 97da74cc6d8f skipped: already exists  
Copying blob d8190195889e skipped: already exists  
Copying blob 17997438bedb done  
Copying blob fdbb043b48dc done  
Copying config b49bc8b603 done  
Writing manifest to image destination
Storing signatures
$ skopeo inspect docker://quay.example.com/playground/release-images@sha256:382f271581b9b907484d552bd145e9a5678e9366330059d31b007f4445d99e36|jq '.Name,.Digest'
"quay.example.com/playground/release-images"
"sha256:382f271581b9b907484d552bd145e9a5678e9366330059d31b007f4445d99e36"
$ oc adm upgrade --to-image=quay.example.com/playground/release-images@sha256:382f271581b9b907484d552bd145e9a5678e9366330059d31b007f4445d99e36 Requesting update to 4.12.3                               
 

$ oc get clusterversion/version -o jsonpath='{.status.desired}'|jq
{
  "channels": [
    "candidate-4.12",
    "candidate-4.13",
    "eus-4.12",
    "fast-4.12",
    "stable-4.12"
  ],
  "image": "quay.io/openshift-release-dev/ocp-release@sha256:382f271581b9b907484d552bd145e9a5678e9366330059d31b007f4445d99e36",    <--- not quay.example.com
  "url": "https://access.redhat.com/errata/RHSA-2023:0728",
  "version": "4.12.3"
}

$ oc get clusterversion/version -o jsonpath='{.status.history}'|jq
[
  {
    "completionTime": null,
    "image": "quay.io/openshift-release-dev/ocp-release@sha256:382f271581b9b907484d552bd145e9a5678e9366330059d31b007f4445d99e36",         <--- not quay.example.com
    "startedTime": "2023-04-28T07:39:11Z",
    "state": "Partial",
    "verified": true,
    "version": "4.12.3"
  },
  {
    "completionTime": "2023-04-27T14:48:06Z",
    "image": "quay.io/openshift-release-dev/ocp-release@sha256:31c7741fc7bb73ff752ba43f5acf014b8fadd69196fc522241302de918066cb1",
    "startedTime": "2023-04-27T14:24:29Z",
    "state": "Completed",
    "verified": false,
    "version": "4.12.2"
  }
]

$ oc get clusterversion/version -o jsonpath='{.status.desired}'|jq
{
  "channels": [
    "candidate-4.12",
    "candidate-4.13",
    "eus-4.12",
    "fast-4.12",
    "stable-4.12"
  ],
  "image": "quay.example.com/playground/release-images@sha256:382f271581b9b907484d552bd145e9a5678e9366330059d31b007f4445d99e36 ",
  "url": "https://access.redhat.com/errata/RHSA-2023:0728",
  "version": "4.12.3"
}$ oc get clusterversion/version -o jsonpath='{.status.history}'|jq
[
  {
    "completionTime": null,
    "image": "quay.example.com/playground/release-images@sha256:382f271581b9b907484d552bd145e9a5678e9366330059d31b007f4445d99e36 ",
    "startedTime": "2023-04-28T07:39:11Z",
    "state": "Partial",
    "verified": true,
    "version": "4.12.3"
  },
  {
    "completionTime": "2023-04-27T14:48:06Z",
    "image": "quay.io/openshift-release-dev/ocp-release@sha256:31c7741fc7bb73ff752ba43f5acf014b8fadd69196fc522241302de918066cb1",
    "startedTime": "2023-04-27T14:24:29Z",
    "state": "Completed",
    "verified": false,
    "version": "4.12.2"
  }
]

While in earlier versions (<4.10) we used to preserve the specified image [1], we now (as of 4.10) store the public image as the desired version [2].
[1] https://github.com/openshift/oc/blob/88cfeb4aa2d74ee5f5598c571661622c0034081b/pkg/cli/admin/upgrade/upgrade.go#L278
[2] https://github.com/openshift/oc/blob/5711859fac135177edf07161615bdabe3527e659/pkg/cli/admin/upgrade/upgrade.go#L278