Medieval English Name Generator

From roughly 1150 onward: William, John, Robert, Richard, Thomas, Hugh, Walter, Ralph, Roger and Geoffrey for men, and Alice, Matilda (Maud), Agnes, Joan, Emma, Cecily, Isabel, Margery, Juliana and Beatrice for women. In the 14th century John, William, Thomas, Alice, Joan and Agnes between them covered well over half of all recorded people.

Not at first. They had bynames that described the individual, such as Roger le Taillour or Agnes atte Gate, which could change over a lifetime. Bynames began hardening into inherited family surnames among the gentry in the 12th century and among ordinary people between about 1300 and 1450, which is why so many English surnames today are medieval trades and places.

Uneasily. Saxon names such as Godric, Aelfric, Eadgyth and Wulfrun survived among the peasantry and the clergy into the 1100s, then faded as families adopted the names of their Norman lords. A few Saxon names (Edward, Edmund, Edith, Alfred) survived because of royal saints. Using a Saxon given name for a character is a quick way to mark them as old stock or low rank in the Norman century.

Very much so. Most English-flavoured fantasy, from Arthurian retellings to grimdark, borrows this exact stock of names, and the real bynames (Crookshank, Makepeace, Strangeways, Drinkwater) give characters more texture than invented ones. Keep the given name real and invent the place in the byname if you need something that does not exist on a map.