One thing you should consider about using full names (like "sha2-256") is that you still have to keep a table. What does "sha2-256" even mean? you know from context. you know that maps to a particular algorithm and particular set of implementations from context.
Writing a table and distributing is cheaper than writing a new implementation of a new hash function and distributing. The "distributing code" part still has to happen.
I think what you would like is if some body (NIST + all others who make hash functions) was maintaining the registry. That's fine, we can give this table onto IANA (though that's harder to update than a PR on Github).