She's not very well-known to people who don't watch this show or people who don't remember all the episodes, but in the fifteenth episode of CardCaptor Sakura Kero-chan was taken care of by a little girl names Akane. It was one of my favorite episodes! "Chau, chau, chau, chau!"
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.
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.