Jinja Honchō, and the Shinto community in Japan in general, do not like abbreviating “Amaterasu Ōmikami” to “Amaterasu”. A lot of people in Japan outside Jinja Honchō do, and often write it in katakana, but Jinja Honchō always writes it out in full.
There are, I think, two reasons for this. The first is the obvious one, that it seems disrespectful to abbreviate the name of the kami. Of course, there are limits to all things: even Jinja Honchō normally refers to Amënikishikuninikishiamatsuhikohikohononinigi no Mikoto as “Ninigi no Mikoto”.
However, there may well be another reason for this. “Amaterasu” is not actually a name. It is not even an adjective. It is a relative clause, meaning “who illuminates the heavens”. Grammatically, using it by itself is nonsensical. “Amaterasu Ōmikami” means “Great honourable kami who illuminates the heavens”, which is not only polite, but coherent. In a recent article from Jingū, the most important jinja enshrining her, in Jinja Shinpō the kami was referred to as “Amaterasu Ōmikami” the first time, but “Ōmikami” after that. This is grammatical, as “Ōmikami” is a noun, but the title is generic, and also used for another kami enshrined at Jingū, so it is not a name for the kami. It is a title with a reference that is clear from context.
This issue becomes even clearer when we look at the way the kami is addressed at Jingū. There, she is called “Amaterashimasu Sumë Ōmikami”. This means “August great honourable kami who illuminates the heavens”, and apart from adding another honorific, it uses a more polite form of Japanese to form the relative clause. However, that means that “Amaterasu” is not part of the way this kami is addressed at her main jinja. Indeed, “Amaterasu Ōmikami” and its variants are not names, but titles.
Does Amaterasu Ōmikami actually have a recorded name? In the Nihonshoki, there are alternate versions of the myth, and in some of these she is called “Ōhirumë (no) Muchi” or “Amaterasu Ōhirumë no Mikoto”. “Muchi” is another title for kami. It is not common, but it is also used for the kami of Munakata, who are called “Michinushi no Muchi”, and in Ōnamuchi, one of the names of Ōkuninushi. “Ōhirumë” appears to mean “Great Daytime Woman”, or “Great Sun Woman”.
This also looks like a title, but pretty much all names that we have for kami take this general form. “Amënikishikuninikishiamatsuhikohikohononinigi” appears to mean “Male kami of the heavens of flourishing rice who brings vigour to both heavens and earth”, for example. There are a handful of kami names that are difficult to interpret, but the general belief is that we have lost all the other examples of the old words (possibly not even Japanese words) from which the names were derived. Ōhirumë has the distinct advantage over “Amaterasu” of being, grammatically, a noun, and so some sources say that Amaterasu Ōmikami’s “real name” is Ōhirumë.
However, there is a strong tendency to not refer to high-ranking people by name in Japan, even today. This is why the Tennō was referred to as “Mikado” (“Honourable Gates”), or why everyone in the eleventh-century novel The Tale of Genji is referred to by a nickname or their job title. This also extends to the author — “Murasaki Shikibu” was not her name, although we know that people at the time nicknamed her “Murasaki”, after the main female character in the novel — for whom it is a nickname based on a flower. Yes, it’s a nickname based on the fictional nickname of a character that she created. There is still debate over what her name actually was, because there is more than one named woman in the historical record who could have been her.
Thus, it is entirely possible that we do not actually have any real names for kami, just polite and indirect ways of referring to them. That is another reason for not abbreviating Amaterasu Ōmikami — to avoid giving the impression that it is a name.