What tradeswoman was baptized by Paul and Silas?

The woman you have in mind is probably Lydia, a "seller of purple from the city of Thyatira" (Acts 16:14). She and her household were baptized in the town of Philippi on Paul's second missionary journey, while he was accompanied by Silas. (You have to look back to Acts 15:40to see that Silas was among Paul's company at the time.)