Naevoleia Tyche was a freedwoman married to a man named Gaius Munatius Faustus, according to Pompeii: The Last Day, by Paul Wikinson. Faustus was a freed slave as well, according to several sources I've found. The couple must have been well off to be able to afford a tomb like this.
"In Pompeii, there is evidence of a particularly successful trader, one Naevoleia Tyche whose tomb survives outside the Herculaneum gate. Tyche was a freedwoman but the style of the tomb which she built for herself and her husband demonstrates her wealth and standing. " Source: "Business Women in Pompeii," Ancient History and Archaeology.
Related: Pompeii: A Study of Roman Tombs and the Freedmen (PDF).