Nayeli

This site says that it means "open" as in "the window is open":

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http://www.native-languages.org/mailbag/nayeli.htm

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This is the complete entry:

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Not exactly. "Nayeli" means "open" in Zapotec, as in "the window is open."

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This is probably a conflation of two different Mexican names. In the Yaqui language (a Uto-Aztecan language of northern Mexico and Arizona), "Naiyoli" means "precious" or "cherished." That is pronounced nye-o-lee and is probably the true source of the name Nayeli.

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The word "nadxieelii" (pronounced nah-jee-ay-lee,) on the other hand, does mean "I love you" in Zapotec (a language of southern Mexico,) and is the source of the Mexican name Nachieli, which some baby name sites may have confused with Naiyoli.

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http://www.native-languages.org/mailbag/nayeli.htm

I am sorry, but this name does not mean 'I love you' according to a trustworthy website which debunks this mistaken belief: http://www.native-languages.org/mailbag/Nayeli.htm

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"Nayeli" means "open" in Zapotec, as in "the window is open." [noted -ed]

I love my name, Nayeli. I have been trying to find more history and origin behind it. My father named me. We are from Mexico DF, city. And my parents tell me it's Naguatle. I believe I am spelling the tribe's name wrong. As I advance in my research, I will post a comment with my findings :)
I should've given my daughter Camila, Nayeli as her middle name. I should change it!