On Designing Women what is the name of first wife?

You are likely thinking of the character Suzanne Sugarbaker from the television show "Designing Women." However, she was never married on the show. She had a long-term relationship with Anthony, her business partner, but they never married.

While Suzanne was depicted as a single woman, the show did explore the complexities of relationships, including marriage and divorce, through the other characters:

* Julia Sugarbaker: Suzanne's sister, was married to JP Horton when the show began, but they divorced during the series.

* Mary Jo Shively: Julia's assistant, was married to Andrew.

* Charlene Frazier: The fourth member of the design firm, was married to Edgar "Ed" St. John but they separated during the series.

It's possible you are thinking of a different character or show. If you can provide more context or details, I may be able to help you further.