A Cyberman, originally known as Ashad, was given the name of the Lone Cyberman.
Originally a humanoid, Ashad had multiple children before undergoing cyber-conversion, transforming him into a Cyberman. As he recalled to the Thirteenth Doctor, his children joined the resistance and so he slit their throats. (TV: The Haunting of Villa Diodati)
Captain Jack Harkness once tried to contact the Doctor to warn him and "beware of the Lone Cyberman" and to not give it what it wants. However, he got hold of Ryan Sinclair, Yasmin Khan and Graham O'Brien instead, initially believing them to be the new Doctor. When he was told that he was she, he told them to warn her instead and tell her about a Fallen Empire. (TV: Fugitive of the Judoon)