People in the Middle Ages—also called the "medieval period," which in Europe denotes the time period from roughly 476 CE to the beginning of the Renaissance in the 14th century—owned pets including dogs, cats, birds, monkeys, and more. Medievalists.net explains that domestic animals were usually not purely for companionship but, rather, typically served some sort of purpose:
Dogs would be used to guard homes or assist in the hunt, while cats were needed to catch mice and other vermin. Still, the relationship between these animals and their keepers was often an affectionate one.
If you're curious about what folks named their pets, you're in luck! Medievalists.net has a very interesting article all about pet names. Turns out some texts from the Middle Ages include names of pets. Here are some examples of dog names from those texts:
In England we find dogs that were named Sturdy, Whitefoot, Hardy, Jakke, Bo and Terri . . .
Geoffrey Chaucer's The Nun's Priest Tale has a line where they name three dogs: Colle, Talbot and Gerland. Meanwhile, in the early fifteenth-century, Edward, Duke of York, wrote The Master of Game, which explains how dogs are to be used in hunting and taken care of. He also included a list of 1100 names that he thought would be appropriate for hunting dogs. They include Troy, Nosewise, Amiable, Nameles, Clenche, Bragge, Ringwood and Holdfast.
And here are some names that were used for cats:
In medieval England domestic cats were known as Gyb – the short form of of Gilbert – and that name was also popular for individual pet cats. Meanwhile in France they were called Tibers or Tibert was generic name for domestic cat in France – Tibert the Cat was one of the characters in the Reynard the Fox animal fables. . .
Old Irish legal texts refer to several individual cats and names them: Meone (little meow); Cruibne (little paws); Breone (little flame, perhaps an orange cat), and Glas nenta (nettle grey).
To read more about pet names, here's the rest of the article. And here's a companion piece featuring Medieval advice on how to take care of pets.
You can learn much, much more about the Middles Ages on Medievalists.net, which states it's "Where the Middle Ages Begin," and which includes news stories, online courses, podcast episodes, book and film reviews, and more. The site explains:
We aim to be the first place people go to when they want to learn about the Middle Ages. Our aim is to offer readers news, articles, videos and more about the medieval world and how that history is presented today.