What's in a name?
"...that which we call a rose: by any other word would smell as sweet." - Shakespeare
The last name Matsumoto is very common in Japan. (I remember plenty of Matsumotos from my class back in Jr. High.) The literal translation of Matsu is pine tree and Moto hints at origin or root, both of which should be pretty self-explanatory.
The first name Rangiku is not a unique one either, though possessing a very fitting image for our character. While Ran means a large number or distortion, Giku (Kiku if pronounced by itself) is the Japanese term for chrysanthemums - one of the most common flowers in East Asia. Simple but elegant, Rangiku is a name that signifies beauty, natural charisma and graceful dignity. Lovely choice for our lady.
I shall not include any sort of Kabalarian definition here. What do they know about the beauty of Kanji characters?
The untold story
I'm going to take a wild guess about the origin of Rangiku's name since no official information was ever provided.
The world of Soul Society is divided into two major areas. The first is Seireitei, where all the Soul Reapers, aristocrats and royalties live. The other is named Rukongai, the place for all wandering spirits to gather and make ends meet by forming small communities or "families". Judging from volume 15 of the manga, Rangiku spent most of her time in a relatively poor Rukongai district before attending the School of Soul Reapers, which means she couldn't have been a born high-class, and she was notably alone.
Here is what I think. In Asia, chrysanthemums are commonly seen at roadsides. What if the name "Rangiku" was inspired by a beautiful flower that happens to be blooming outside of a Rukongai house? Sure, chrysanthemums are random and simple flowers, but beautiful enough to please the majority. Meanwhile, this name also symbolizes Rangiku's future position in society: a girl who'd eventually grow into a beautiful woman, liked and admired by everyone.
Hitsugaya mentioned once that most Rukongai babies don't know their exact date of birth and would make up his/her own birthday based on important dates in their life. The same applies to Rangiku, though September is a good month to take for her birthday either way: it's when the chrysanthemums start to bloom! In other words, while we don't know who named Rangiku and why did the person decide on such a name, it's not hard to guess what might have gotten into Kubo's head at the time of Rangiku's character design ;)