My real name is Eiko, and I've always wondered what it really means, and how to write it in Japanese. I took Japanese for 4 years in high school, and my teacher didn't know either. When I look it up I get many different answers. When I type it into a hiragana dictionary or look it up in a Kanji/Japanese-English dictionary, I get many different answers.
Therein lies your answer - there are a lot of possibilities for the meaning. Since people can chose the kanji for names, there are a lot of different ways to write Eiko - the most popular that I can think of are 栄子、英子、映子、瑛子、暎子、恵似子、永子、 and 詠子. The 子 that appears in all of them has the meaning 'child,' and is very common in female Japanese names (especially between 1950 and 1970, if I remember correctly). The rest are easily looked up as well. My advice would be pick what you like and go with it!
I learned something interesting recently which is that names were given in Japan without kanji for quite some time pre-war. So it's also possible, that your name doesn't refer specifically to any of the kanji-based combos. The same thing affects my mother-in-law and my wife regarding their names (as Japanese Americans).
not just pre-war, either - I had several elementary school students in Japan over the past several years who had names that 'normally' would have kanji, but were written just in kana.
