OK, with katakana the goal is to approximate the pronunciation as closely as possible. I think the katakana translator didn't really know how to handle it, and the result may not sound right to you:
モイクワル (you can click on this link and hit the "listen" button on the Japanese side to hear how this is pronounced).
So, is "Moi" is pronounced like the English "me" or the French word that means "me"?
In the former case, I would say in romaji (Japanese pronunciation with the alphabet), the first vowel would be shorter and not elongated, miku-ru (the dash denotes a long vowel. There's no syllable-final "L" in Japanese, so it would be approximated to "ru." In Katakana this would be
ミクール
If it's the French pronunciation, that first character would be replaced with something more like モア "moa,"
モアクール
For Naked Illusion, the katakana translator did OK, though I would probably write
ネイキッド・イルージョン, neikiddo iru-jon, favoring more of a dipthong in the first syllable of "naked" than a drawn-out, flat "ne-." Both katakana spellings seem to be used, although in different contexts for some reason. It doesn't make a huge impact on how it sounds, so this could be up to you.
Both pronunciations together for comparison.
If you wanted that written in kanji, there may be a few different ways to write it (perhaps
@Toritoribe would be a better translator), but it would be pronounced completely differently and maybe have some nuance you didn't intend. I would stick with the katakana, as anyone who could read katakana would be able to pronounce the company name correctly.