Why was Anne Frank named Anne?

The name of her father was Otto Heinrich Frank.

That's why Frank.

her real name was 'Anneliese Maria Frank'

Why Anneliese Maria?

That's not clear to me. Maria is a popular catholic name but based on the Jewish literature.

Annelies or anne. It seems that there is no explanation for the first name.

That's not that strange in the Netherlands. Many names are choosen because people like the sound of it. Just like Margot, her sister.