In Hebrew a ladybug is known as פרת משה רבנו lit Moshe Rabeinu's cow. Just why the modest ladybug has earned this highest of accolades remains shrouded in mystery. A few years ago while reading this weeks Parsha (חקת) I believe I came across a likely origin for the name, which no one else seems to have picked up.
Chukat deals with the laws of the Red Heifer:
ב זֹאת חֻקַּת הַתּוֹרָה, אֲשֶׁר-צִוָּה יְהוָה לֵאמֹר: דַּבֵּר אֶל-בְּנֵי יִשְׂרָאֵל, וְיִקְחוּ אֵלֶיךָ פָרָה אֲדֻמָּה תְּמִימָה אֲשֶׁר אֵין-בָּהּ מוּם, אֲשֶׁר לֹא-עָלָה עָלֶיהָ, עֹל.
2 This is the statute of the law which the LORD hath commanded, saying: Speak unto the children of Israel, that they bring thee a red heifer, faultless, wherein is no blemish, and upon which never came yoke.
Rashi comments on the words "Bring Thee" - Forever it shall be called on your name. What seems to be troubling Rashi is why does the commandment seem to be focused on Moses specifically (i.e why does it not just say "Take a cow" but says they should take it to Moses). His answer is that this Mitzvah will always be associated with Moshe.
So what would a Heifer named after Moshe be called? Moshe Raveinu's cow! If this midrash is to be accepted, then all red cows, were probably nicknamed "Moshe Rabeinu's cow".
It is not a large leap of the imagination from a Red Heifer to the ladybug. Both are red, and the ladybug has spots like a cow. Hence I speculate that over the centuries the ladybug got the nickname of the Red Heifer, but the origin has been forgotten.