A few points to make here:
- There is no single radical that represents both 人 and 入. They are different radicals, and thus they rightly have different names.
- 𠆢 is officially treated as a variant of 人, and has nothing to do with 入.
- You cannot arbitrarily break down characters and expect the decomposition to be meaningful***. Furthermore, even if you do break down characters, the broken down components do not necessarily map onto radicals.
There is some misunderstanding about what a radical is; it is a section header (literal translation of 部首) in a character dictionary, and there is only one radical for each character, as each character is only listed once in any given dictionary under a section header. This is akin to English dictionaries, where for each English word, there is only one first letter under which it would be grouped in a dictionary. This obviously means that it is incorrect to refer to the following characters with the 𠆢 radical:
- 鉛 (radical 金)
- 飲 (radical 食)
- 琴 (radical 玉)
- 吟 (radical 口)
- 冷 (radical 冫)
- 倹 (radical 亻)
Since the historical development of the characters are quite obscure without some thorough understanding of Chinese paleography, different dictionary composers throughout history have broken down the characters in a different manner, and thus different dictionaries throughout history may have different sets of radicals and may group the same character under different radicals. This means that questions with ambiguous answers like "What is the radical of 全? 人 or 入?" are ultimately meaningless; the radical of X is whatever the dictionary you're looking up X in says it is. Some dictionaries list 全 under 人, and some list it under 入.
In practice, Japanese dictionaries usually inherit the set of radicals from the Kangxi dictionary, so there is fortunately a fairly large amount of consistency between dictionaries.
***Here are some examples to get an idea how characters actually break down (if at all).
- 金 originally depicted a heat-resistant container used to melt metals (crucible), and cannot be broken down into components like 𠆢 (note that even dictionaries do not break down 金; it is its own radical)： . However, there is a hidden phonetic cue in 金 (the phonetic cue is 今), which originally appeared in the upper portion of 金.
- 食 originally depicted a mouth 亼 (this was originally 口 written upside down), and a container for grain 皀, with the compound meaning 'eat': . Note that in dictionaries it is also its own radical and does not contain 𠆢. The modern form, while looking like 良 or 艮, actually has nothing to do with either of them.
- 今 originally depicted a mouth 亼 (see previous point) which has been closed off , indicated by an additional horizontal mark on the bottom. It eventually morphed into something like , by then making it easier to see its connection with 金. The character is a phonetic loan; its modern meaning ("now, the present time") is unrelated to the original. Despite it commonly being grouped under the 人 radical, it is not derived from it.
- 介 actually contains 人; it originally depicted a person 人 with two marks on either side, and has variously been used to denote the meaning boundary (bottom component of 界; the two marks were drawn by the person, indicating the person's boundaries), armour (modern compound 介甲; the two marks indicated wearable armour), or a contagious skin disease (modern character 疥; the two marks were abstractly used to denote the disease).