From Wiki:
The song is one of a number Brown wrote about Renée Fladen-Kamm, the then-girlfriend of The Left Banke’s bassist Tom Finn and object of Brown’s affection. She was associated with the band for a few weeks, and was described as a free-spirited and tall blonde.
The song was written one month after Brown met her. “Walk Away Renee” was one of a series of love songs the infatuated Brown wrote after meeting his newfound muse.
Other songs written about her include the band’s second hit “Pretty Ballerina”