According to the Wikipedia article Radical (Chinese characters), the Chinese name for radical is 部首 (bùshǒu; literally "section header"). The term appears to originate from the 2nd-century dictionary 說文解字 / Shuōwén Jiězì. Another term I've seen is 偏旁 (piānpáng), e.g. on Wikibooks.
However, what I'm mainly interested in are Chinese names for different categories of radicals (if such names are in use), i.e.
- semantic components such as 氵for water and 亻for human being,
- phonetic components,
- components such as 丿, which are used as radicals in dictionaries (for lookup purposes) without having a meaning of their own.
I'm mainly interested in the Chinese term for the fist category, since that category is probably most helpful when learning Chinese characters.