There's a lot of names to deal with in your original post.
We would transliterate רִבְקָה into English as Rivka or Rivkah according to the rules of the Academy of the Hebrew Language. The LXX translators transliterated it into Koine Greek as Ρεβεκκα (cp. LXX Gen. 24:15).
We notice the following:
1) The chirik nikkud under the Hebrew letter ר is transliterated into Greek as an epsilon (ε), which represents the /e/ phoneme.
To me, this isn't much of a stretch. There was probably some phonetic overlap between these two vowels.
2) The shva nikkud under the Hebrew letter ב is transliterated into the LXX as an epsilon (ε), whereas we wouldn't transliterate into English in that particular word.
If I am not mistaken, that's a shva nach, which is unvoiced. So, why did the LXX translators transliterate it? It may have been voiced during that era. Or, the translators of the LXX didn't appreciate the idea of this consonantal cluster: βκκ. So, they decided to transliterate the shva so there would be an epsilon between the beta and the two kappas, i.e. Ρεβεκκα. Or, during that era, the shva nach may have been even slightly voiced, whereas today, it is said to be "unvoiced." Or, well, let's be honest, there was no such thing as a shva nach back then, as diacritics were not added until about a millennium later. So perhaps they did pronounce a bit of an /e/ phoneme between the ב and the ק when they said the Hebrew word רִבְקָה. These are just my guesses. A more comprehensive analysis will examine words which possess shva nachs and then analyze their transliterations in the LXX. But, that's a laborious effort.
3) The Hebrew letter ק is transliterated as the digraph κκ.
This may be due to the fact that the ק was articulated at the uvula rather than the velar region of the oropharyngeal tract as it is today. In modern Hebrew, there is no phonemic distinction between the letters כ and ק. Both are pronounced as the phoneme /k/, a voiceless velar stop. However, in Arabic, the equivalent letter ق is pronounced as the phoneme /q/, a voiceless uvular stop. It's quite possible that this was the ancient pronunciation of the Hebrew letter ק. As a result, it would not be transliterated into Greek as κ but κκ. Again, this is my speculation.
4) The ה is not transliterated.
This is no surprise as the /h/ phoneme does not exist in Greek except for the "rough breathing" (δασὺ πνεῦμα) which only occurs at the beginning of some Greek words. Since the letter ה is at the end of the word רִבְקָה, it is simply not transliterated into Greek. There are multitudes of examples of this phenomenon in the LXX. (By the way, this is why אהרון is transliterated into Greek as Ααρων.)
Maybe in the future I will examine more Greek transliterations of Hebrew words in the LXX, but this is all I can surmise for now. Not looking for a best answer. I am just interested in your question and thought I can share some thoughts.
Edit: I do want to tackle one more though: יצחק. We would transliterate that into English as Yitzchak. But, in antiquity, the Greek letter ι and the Hebrew letter י probably represented the same phoneme when located at the beginning of a word, i.e. /j/, a voiced palatal approximant.
So, the י in יצחק is transliterated as the letter ι. The צ does not have an equivalent letter in Greek. The translators probably found it most similar to the Greek σ. The ח is not transliterated, just like the letter ה, because Greek lacks an equivalent. And, finally, the ק is transliterated as the letter κ, as can be expected. So, I can actually see how יצחק became in Greek Ἰσαάκ. Of course, in English, we write "Isaac" because of the Greek, not because of the Hebrew. If we were to actually transliterate the Hebrew, it would be Yitzchak.