Akane

This name also means 'Madder' (Aka - red, ne - root), and this is the meaning used for Akane Tendo in Ranma 1/2.

I read somewhere, in a Japanese dictionary, that this name also means "madder", as in the flower.

Also is a name of a deep red flower.

The definition is correct, but I just want to point out that there is a more commonly used name pronounced Akane written with a different character, one that means "walk" as in to walk one's own path.

Akane is usually written with the kanji for 'deep red'. But there are many different kanjis for the name, for example Akane can also be written as 'Peaceful Flower Sound', etc.

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I don`t know a kanji that means 'walk own path' that can be pronounced Akane. Ayumi means 'counter of own steps' or 'walk', but I don't think Akane does.