Quite self consciously named her band after herself - 'Machi-kara' means from the city (machi), and she now writes the Japanese character for city for the 'Machi' character in her name.
The band name could mean 'from Machi(as in Machiko)', so it's one of the vainest band names I've heard. Some Japanese people don't even know this connection.
She's basically Japan's version of Avril Lavigne. But she writes her own songs :P