I am looking into how to produce an item with a custom image.

I can see where I would change the image in the production menu but there is only one image available to select.

How can I choose a public image when producing?

you dont, public customs are applied via the CP exchange on an entity already in existance

According to rules page on datacards

“ 4/ Custom Datacard Images
Datacards can have custom images purchased for them so they produce the custom image instead of the default. Once set, you have the option of turning the image on and off for production via the production menu. There is a one time fee to set a custom datacard image of 5% of the Raw Material Price (RMP) of the entity on the datacard, with a minimum of 2,000credits. Both regular and large images can be set, and all images are reviewed by the art team before approval. The form to set an image is located under the "Assign Datacard" form  ”

And Also Rules page for Production

“ 1.2.7/ Custom Datacard Image
You have the option of assigning a custom image to the datacards you own. There is no need to retool or otherwise alter the production process when the image is accepted. Once set, any entities produced with that datacard will have the custom image set for it instead of the standard image. When adding a project to the queue, or editing one that hasn't yet started, you may choose to use the default image instead of your custom image. For more information, see Datacards: Custom Datacard Images  ”

Unless this has not been implemented or is a Public custom Image not 'custom' ??

The "Public Images" are just for CP-assigning of a custom image as Ichiru mentioned. THIS LINK for custom image application to a single entity.

They aren't the same as the "Custom Datacard" images that factions can pay for and upload after approval.

Ok so that makes sense. How does a faction submit artwork for a datacard then. I don't see an option for it anywhere.

There used to be an option in the DC page I believe. However when we transitioned the custom images to be hosted by SWC that functionality was lost. I'm not sure if it has been restored. You could ask Jevon as the Art Leader he would be the best person to ask since he might be able to manually add an image if there is no function to do so on the players side.

Ellias i believe the custom DC thing is now the faction customs on the CP page, i think they pay a one time CP fee and can apply that image to assets of that type they produce

Hmm, does that actually apply to the DC? I remember the Faction option used to do something like treat the faction as a player and allow those custom images to be available for members with appropriate privs. Or at least it didn't used to apply a custom image to the DC for use for free when producing.

If that is how it is, that is good and probably a good idea to ask for a rules update.

As far as I know custom images on DCs do not work anyway. Its been a while I tried it but I haven't seen any Sync update mention it works again.

Faction customs are what DC customs is supposed to be now. Though I cannot comment on their current functionality.