You insinuated that you disliked the name "Mini Rini" as if in general, not specifically as a hypothetical dub name for Chibi Chibi, thus Frenchfries pointed out that you should thus dislike the name "Chibi Usa" as well. You said the thought process behind it made sense, which is what prompted my reply. This could have all been avoided had you made your comments clearer.
If you're okay with "Sailor Mini Moon" because it makes sense for the English language, I don't get why you'd dislike "Itsy Bitsy" or "Teeny Tiny," which replicate the sense of "Chibi Chibi" in English.
Chibi Chibi may not be a "mini Rini" but her name explicitly comes from Chibi Usa's (the result of her repeating the first half of that name). The characters didn't look at this unnamed strange toddler and say, "Wow, she's *so* little, let's call her little (Chibi) twice!" Since "Chibi Chibi" is just a stand-in/nickname for her anyway, and she bears an obvious resemblance to Chibi Usa (to the point they briefly speculate she might even be Chibi Usa's future daughter), their deciding to call her "Mini Rini" would make complete sense.
Just had to get that off my chest. With that, I'm done with this tiresome discussion.
To return to the more interesting elements of this thread's topic question...
I wonder what the dub's version of the Three Lights' songs would have been like. And would they have done a new theme song based on "Sailor Star Song" or continued to use "She is the One Named Sailor Moon"?