In early version of the draft, it seems that "Taiwanese Kana" is also proposed as the name of the block.
I would second the proposal to use "Katakana Phonetic Extension Extended-A" as the block name for the following reasons:

Some of the extensions has also been used for other languages. In Taiwan, they have also been used to write Hakka in Taiwan.
(Note that during the Japanese ruling period, the language is referred as 廣東話 (Canton language) but it actually means Hakka, not Cantonese. This is because Hakka in Taiwan are mostly originally from Canton area.)
The Hakka Kana literature is much less than Taiwanese Kana. But they do exist. (also related to the name of the tone mark, see another issues.)

I also known that Kana has been used to write Fuzhou https://en.wikipedia.org/wiki/Fuzhou_dialect but with even less literature.

I would suggest to consider other possible naming scheme for the tone mark. Currently, the tone number (2,3,4, etc) is using Taiwanese convention. However, when they are used to write Hakka, a different mapping is used.

For example, Taiwanese tone two mark (U+1B302) is to represent tone three in Hakka. (I don't have the complete mapping in hand.) So it might cause confusing if they are named as "tone two" etc.

I don't have good suggestion for alternatives, but maybe something similar to the IPA tone letters in Unicode.
(EXTRA-HIGH TONE, etc https://en.wikipedia.org/wiki/Tone_letter )