What is the name of the Japanese film series about a girl whose father works at a train station and she grows up and looks for her mother?

The Japanese film series you’re referring to is called "Kiki's Delivery Service." However, it's important to note that the plot you described more closely resembles the film "Aruitemo Aruitemo" (also known as "Still Walking"), which explores family dynamics and themes of loss. If you meant a different series, please provide more details.