RFC 5952 gives you the canonical IPv6 format. That is explained in the RFC itself:
This document defines a canonical textual representation format.
and
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 hexadecimal notation.
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.
The slash notation is another way of writing the subnet mask. It works the same for IPv4 and IPv6.
The number /3 indicates the number of consecutive 1's in the mask. Since the mask is the same size as the address, that means that for IPv6, the subnet mask is three 1's followed by 125 0's (3+125=128 bits).
For an IPv4 address it means three 1's followed by 29 0's (3+29=32 bits). It can also be written as 192.0.0.0.
Best Answer
There are some common use cases:
::ffff:192.168.0.1This is used in software that uses IPv6 sockets even for handling IPv4 connections. That makes it easier to write software because everything looks like IPv6.
64:ff9b::192.168.0.1This is the NAT64 well-known-prefix. These addresses are NATed to IPv4 by a NAT64 gateway. It is used to let devices that only have IPv6 reach IPv4 destinations.
It can be used with other prefixes as well. For example not all NAT64 gateways use the well-known-prefix. And there are other protocols that embed IPv4 addresses in IPv6 addresses or prefixes. The two mentioned above are the most common though.