Why were so many important figures in Tudor England named Thomas?

I actually recently answered a very similar question. I'll excerpt from my answer there with a couple changes:

Yes, popular names in the late Middle Ages/early Reformation really tended to cluster. Consider that 50% of Henry VIII's wives were named a variety of Catherine and 33% of them Anne. (And Anne Boleyn's father, maternal grandfather, and uncle were all Thomas.)

In some cases it's simple generational transfer--Anne's uncle Thomas Howard is the oldest son of Thomas Howard. The zeitgeist for the popularity of this particular name, however, is almost certainly the cult of 12th century bishop-martyr-saint Thomas Becket. (Latin cultus, devotional practices surrounding a particular saint or Church celebration like prayers of intercession, dedicated sermons and hymns, pilgrimages to a shrine, etc.)

Possibly after St. George (England's patron saint), Thomas Becket was the saint of late medieval England. The popularity of martyr-saints towards the end of the Middle Ages (in conjunction with a lack of new actual martyrs) only promoted Becket's popularity. Recall that Chaucer's pilgrims are en route to Thomas's shrine at Canterbury. He usurped a place for himself alongside Paul as co-patron saints of London. Parish and civic guilds frequently adopted him as their patron saint. While plays revolving around saints' lives and miracles weren't as common in England, there are actually quite a few examples of Thomas ones from the late fifteenth and early sixteenth centuries. They were popular enough among potential audiences that they're noted to serve as fundraising events for some of those guilds! And Thomas's murder certainly brought the entertainment. Surviving records note payment to a local laundry for washing Thomas's "blood" off the vestments worn by the actor during the martyr scene.

As to Henry's wives, St. Anne (Grandma Jesus) and St. Katherine (of Alexandria, primarily, although 14th century Italian saint Catherine of Siena was also popular in certain circles) were two of the most important female saints by the end of the Middle Ages.