In Claudia's single, professional lawyer life, her last name is Parks. In her suburban mom life, her last name is Mills. The central plot line for both "lives" is a court case fighting either for or against the Stross Company's plan to put a mill in the suburban park. Her last name in each life reflects what she is fighting for in the opposite life.
The house belonging to Claudia and Bill is quite prominently numbered "9120", a reference to Daphne Zuniga's previous show "Melrose Place" (which was a spin off of "Beverly Hills 90210" and also took place in the 90210 area code).