I personally love the names Yumi and Yumiko. Though "Yumiko" is not on this site, and on another I found it meant "beautiful child." I thought it would have meant "bow child" or something, because of the use of the suffix "ko" which usually means "child."
Again, many possibilities for this name (depending on the kanji).
"yu": -kind -freedom (I think they also use this character for "bow", but I'm not sure) -together/friend (rare, but I did meet one Yumi who used this kanji... though the name would normally be pronounced Tomomi in this case) -bear (produce... as in produce fruit) -kind/smart
This is a really cool and pretty name. And I love it. Only, one of the main characters from Code Lyoko has this name. And I really really really really hate that show. -grabs knife-
Yumi, when used as a name, refers to "yu" meaning bow, and "mi" meaning beauty, to combine together making "beauty bow," or "beautiful bow. [noted -ed]
Yumi was the name of the young alien girl character in the 1980s English-language anime kids' show "Ulysses 31". Her older brother was named Numinor (which is curious in itself as Numinor is a place name used by both J. R. R. Tolkien and C. S. Lewis).
When using the kanji bearing the meaning of "friend", if one chooses to pronounce it "yuu" rather than "tomo", then it's "yuu" with a long "u" and not "yu" as the yu in Yumiko. So that would be Yƻmiko. It may exist, I can't be sure, but I don't think it is really used.
I like Yumi, and I think it has a sweet, simplistic and pleasant sound. But what I like most about it is the look of the kanji it is written with - 弓. It looks like what it means. Simple, curved, elegant and arched - an archery bow. Which makes it much easier (for me) to remember and draw than many other characters. I also like Yumi spelt 弓美 (because I find "beautiful bow" prettier than just "bow") and 夕美 - evening beauty, which I think has a mysterious and poetic feel to it.