We don't have specific words for kanji or radical reduplication, bacause it's merely coincidence, or a side effect happens when we put related or the same words together.
As for repeating the same words, we call it 畳語. If a word that written in a single kanji is repeated, it appears as if the kanji is repeated. But if you try with other words, you'll get 場面{ばめん}場面{ばめん} (or 場面々々) "situation by situation", 知{し}らず知{し}らず "unconsciously" or ぴかぴか "glitter-glitter", too.
Categorizing words whose components have the same radical is generally not as good an idea as it seems to be. I won't deny its use for mnemonics, since radicals with strong semantic restriction (like 木, 虫 or 魚) may create more same-radical (dvandva-type) compounds, but as a whole, we don't think coincidence of radical itself is associated with some essential nature of our writing or language. Radicals often only shed light on their meanings from one side; 機械 both have radical Tree, but today's people easily notice that it's starting to deviate from what it's supposed to mean. How 消滅{しょうめつ} "vanish" is related to Water(*1), and how 陰険{いんけん} "sly and mean" to Cliff(*2)? Actually, they're examples two characters of one radical happened to be brought together, irrelevant of what the radical meant. 明日 is more like false positive; 明's 日 "sun" is historical simplification of 囧 "window". A similar case is 鮮魚{せんぎょ}(*3) "raw fish". Although these words share the same radical, you'll see graphically unrelated 鮮明{せんめい} "vivid" shows far much semantic relevancy with each other.
There is, however, a small number of words that yield same-radical compounds with high probability. 葡萄{ぶどう}, 混沌{こんとん}, 齟齬{そご} and 魑魅魍魎{ちみもうりょう} all belong to 連綿語. For instance, 葡萄 "grape" both have Grass, because they put it intentionally to make sure it refers to a plant. (Neither 葡 nor 萄 is used outside "grape" or transcription of Portugal, 葡萄牙.) These words had their sounds in multiple syllables first, then got their kanjis later. Basically it's a matter of Chinese that affecting Japanese writing too.
*1: 消
originally meant "rivers run dry", and 滅
meant "annihilate" in its bare form 烕
. Why 滅
has got Water is not clear, but probably was association with its another meaning: "extinguish fire".
*2: 陰
means "overcast, dark". It got Cliff while heavily used to mark place names in mountains' shade (north) side. 険
's one just came from one of its meaning: "precipitous pass".
*3: 鮮
originally meant a name of fish. Using it for "fresh, lively" is a kind of rebus.