RFC 5952 gives you the canonical IPv6 format. That is explained in the RFC itself:
This document defines a canonical textual representation format.
4. A Recommendation for IPv6 Text Representation
A recommendation for a canonical text representation format of IPv6
addresses is presented in this section.
There are people who incorrectly call a fully uncompressed (eight words of four hexadecimal digits each) the canonical format but the RFC refer to this as conventional notation.
When zero words are replaced with
:: it is a compressed address format, and when used with IPv4 notation, such as
::ffff:10.11.12.13 it is a mixed, or compressed and mixed, address format.
Edit based on the question edit:
There is no official name for the IPv6 notation, but RFC 5952, among others, refers to it as
Even the IPv4 address notation commonly called
dotted-decimal notation is not really in any RFC defining IPv4. It is mentioned in RFC 3795, Survey of IPv4 Addresses in Currently Deployed IETF Application Area Standards Track and Experimental Documents, an informational RFC which specifically states:
This memo provides information for the Internet community. It does
not specify an Internet standard of any kind.
In conclusion, there is no official name for the general IPv6 format, and you may call it whatever you wish. I think it is important to distinguish between the various IPv6 address formats. My company has a requirement to use the RFC 5952 canonical format rather than the conventional format.
Note: I left the rest of my answer in as useful information.