More than two decades ago, when Melly Barajas Cárdenas and her father were on vacation in Mazamitla, Mexico, he told her that he wanted a tequila made in his name. At the time, Ms. Barajas Cárdenas was a clothing designer in Guadalajara, where she is from.

“I didn’t know anything about tequila,” Ms. Barajas Cárdenas, who declined to give her age, said in a recent telephone interview conducted in Spanish. “But it was my father’s wish.” So she decided she would find a way to fulfill it. She knocked on doors, asking various tequila producers for help, and eventually found one who produced a line of bottles for her.

Ms. Barajas Cárdenas quickly realized she wanted to do more.

“At first, it was a goal I had to accomplish, more than something that I wanted to do,” she said. “My clothing business was very comfortable. I went to the office, went home, it was easy. But once I was in the tequila industry, I loved it. The smell, the taste, it was marvelous.”