Why call this "distribution"?
This is going to be impossible to Google.
How many people are setting up their own container registries?
This doesn't need a catchy name. It's a piece of "if you're the person deploying this, you already know us" infrastructure, similar to Enterprise-grade hypervisors or Internet backbone switches.
it's not about "catchiness", it's about being able to have a unique moniker, so whoever is searching for it can find it. "Distribution" immediately is going to clash with the multitude of linux distributions. They could have named it "image-distribution", "container-image-distribution", "cidistribution", whatever.. just something that makes it easier to find via search.
...which is what I meant by "catchiness": the ability to have a context-free unique name. Not all products need context-free unique names. Heck, not all products even need names.
ISO/ANSI standards and RFCs, for example, are just numbers. You can actually Google the most famous of these ("9001" gets you the ISO standard; "2616" gets you the RFC; etc.); but on average this doesn't work, because those numbers are small and collide with other meaningful numbers in other namespaces†. (Things like electronics part numbers, for example.)
With any of these identifiers, the thing you do instead of just punching the ID into a search engine, is to first search for either 1. the website of the entity you know owns the thing, or 2. some kind of "catalog" site; and then plug the otherwise-non-unique identifier in there. Your identifier, despite not being unique generally, is unique when put in the context of a domain-specific keyspace.
In this case, the keyspace is "CNCF projects", or maybe "implementations of OCI specifications." The specification for these registries is called the "OCI Distribution" spec, just like the specification Docker containers obey is the "OCI Container" spec.
Look at the list of Apache Foundation projects: https://projects.apache.org/projects.html — how many of these have names that have no hope of being searched unless you know to prefix "Apache" to them? Chemistry? Drill? Flex? Portals? Streams, for goodness sake?
And this is why I said that it wasn't important because only very specific people need to stand up their own container registries: all those people already know enough about container registries to intuitively prefix "Docker" or "OCI" or "CNCF" on their search query; or to go to those projects and navigate from there.
This would be a problematic name if random people needed to install it after a word-of-mouth conversation. But they don't, any more than random people need to find the manual for the exact model of Juniper network switch in their ISP's head-end. Only their ISP's network engineer needs to do that—and that fellow has had rather a lot of exposure to Juniper products, and so likely already has their support site bookmarked. (And probably has the physical copies of the manuals, too, if they still print those.)
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† Tangent: it'd be a fun project/blog post, to go through the Google search results for the search-terms "0" through "9999", and categorize the top results by keyspace. How many times do RFCs "win"? Etc.
Contrast that when I go to the Docker distribution github page the url is https://github.com/distribution/distribution. You don't see anything wrong with that nomenclature? I'm the only one?