The only Lord in The Taming of the Shrew is in the Induction and is called "a Lord". We know the name of his page and of five of his dogs, but we don't know his name. None of the characters of the play itself are noble enough to be called "Lord".
katherine
In "The Taming of the Shrew," Katherine's full name is Katherine Minola.
Katherina Minola, sometimes known as Kate.
The father's name is Baptista.
Minola
It's really Hortensio in disguise under the false name of Licio.
It doesn't give his surname, but we know that his father's name was Antonio and that he came from Verona.
The name Minola means clever. The name is a boy name and was also used in Shakespeare's works and meant taming of the shrew.
Hamlet, Romeo & Juliet and Macbeth are by far the three most famous ones. There's also All' Well that ends Well, A Midsummer Night's Dream, The Taming of the Shrew, Othello, Julius Ceasar, Much Ado about Nothing and Antony & Cleopatra.
The headdresses that women wore at Shakespeare's performances were called "headpieces" or "coifs." These headpieces were often elaborately decorated with jewels, ribbons, and feathers to denote the social status of the character being portrayed.
Romeo and Juliet and Taming of the Shrew both contain young lovers in Italy.
He doesn't have one. Not all cultures use the given name + family name pattern you are used to. Sometimes people only have one name.