So I was thinking about how to talk about these characters in a culturally-neutral way. Chinese seems to be used, but it implies a particular way of writing characters (not to mention it makes it sound like you're ignorantly conflating East asian cultures).
Those scripts are usually referred to as the Chinese family of scripts:
Chinese family of scripts are writing systems descended from the Chinese Oracle Bone Script and used for a variety of languages in East Asia. They include logosyllabic systems such as the Chinese script itself (or hanzi, now in two forms, traditional and simplified), and adaptations to other languages, such as Kanji (Japanese), Hanja (Korean), Chữ nôm (Vietnamese) and Sawndip (Zhuang). More divergent are Tangut, Khitan large script, and its offspring Jurchen, as well as the Yi script and possibly Korean Hangul, which were inspired by Chinese although not directly descended from it. The partially deciphered Khitan small script may be another. In addition, various phonetic scripts descend from Chinese characters, of which the best known are the various kana syllabaries, the zhuyin semi-syllabary, nüshu, and some influence on hangul.
This name goes in the same vein as the Brahmic family of scripts, the term used for the Brahmic scripts used in India and East Asia.
For Unicode purposes, they're referred to as CJK ideograms, short for "Chinese, Japanese, and Korean". This is kind of awkward, and not something I've ever heard used in normal conversation, but Unicode is a decent precedent for politically-neutral usage.
The name I've heard more often in actual usage, if you want to avoid the word "Chinese", is Han characters or Han logograms, a direct translation of 漢字/hànzì/kanji/etc. This is most often used in cases where the speaker wants to distinguish the characters in general from the specifically Chinese usage of them, as in "Han unification" (the process of unifying Chinese, Japanese, and Korean variants into a single Platonic ideal of each character).
“Heterograms” is a general term for characters/spellings belonging to one language which are used to represent a non-cognate word with the same meaning in another language. For example, there are Sumerian heterograms in Akkadian, Hittite etc., Aramaic heterograms in Middle Persian, Sogdian etc., and some others. For that matter, there is also “&” (ligature for Latin “et”) to represent English “and”, or “lb” for “pound”. These too are heterograms.