Yumi

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 Yûmiko. It may exist, I can't be sure, but I don't think it is really used.

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]

Again, many possibilities for this name (depending on the kanji).

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"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

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"mi"
-beautiful
-fruit

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Variations with Yumi:
Yumi
Yumie
Yumika
Yumiko

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."

Means a bow as in "Archery Bow", not "pretty pink Bow".