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In other words, are there kanji, which can only be used as a part of a kanji compound and/or with okurigana?
For example:
Is there a kanji where (1) is not an option?
If there are such kanji, do they have some special name?
Yes there are, but it is a grey area if you include rare, uncommon, creative or archaic readings.
People can be creative especially when it comes to kun-readings. Even for a kanji usually used only in compounds you might find a stand-alone usage if you're looking hard enough. Some of these need okurigana, eg. 隷う【したがう】 or 悠か【はるか】, but some don't, eg. 英【はやぶさ】.
Additionally, there are some on readings that are rarely used as a word, eg. 感 or 奏 or 了, although it could be argued sometimes only as part of some (more or less) fixed expressions. The same applies to 見 as well, 見【けん】 is not a common "word", but you can find it in expressions such as:
それは皮相【ひそう】の見【けん】である
That's a rather superficial view of things.
A Japanese name could be 非単漢字, but that's more like a description, and not exactly common.
If you're looking for a technical term, it is called word. I know it sounds simple, but effectively you are asking whether there is a kanji that cannot be used as a word by itself without further glyphs (kanji or kana).
A word is a unit which is a constituent at the phrase level and above. It is sometimes identifiable according to such criteria as
- being the minimal possible unit in a reply
- having features such as
- a regular stress pattern, and
- phonological changes conditioned by or blocked at word boundaries
- being the largest unit resistant to insertion of new constituents within its boundaries, or
- being the smallest constituent that can be moved within a sentence without making the sentence ungrammatical.
A word is sometimes placed, in a hierarchy of grammatical constituents, above the morpheme level and below the phrase level. source: SIL Linguistics
見【けん】 is not a word as in that you can just say or answer 見【けん】です ("it is a view") and expect people to understand.
Some kanji I can think of, mostly used only in one compound, with no kun-readings by themselves:
蝙蝠 (bat, the animal), 蟷螂 (mantis), 髑髏 (skull), 躊躇 (hesitate)
But rarely: 蝠【まむし】, 躇む【ふむ】, 躊う【ためらう】
Some more kanji if we don't count okurigana:
乖 (eg. 乖離), 擁 (eg. 抱擁), 倣 (eg. 模倣), 避 (eg. 回避), 喚 (eg. 叫喚)
