Gertrude
Her name was Gertrude. A complete list of characters in any Shakespeare play and their relationships can be found in the Dramatis Personae, which will be at the beginning of most editions. We never learn anybody's last name.
William Shakespeare's mother's name was Mary Shakespeare
Shakespeare's mother was Mary. She was an Arden before she married John Shakespeare.
Mary Arden was Shakespeare's mother's maiden name. I do not know what her maid's name was.
Anne Shakespeare was William Shakespeare's sister. Their mother was called Mary Shakespeare. Anne Shakespeare was also William Shakespeare's wife. We don't know her mother's name. She had a stepmother called Joan Hathaway.
Mary Arden was her name. And You can see for yourself at http://www.william-shakespeare.info/william-shakespeare-biography-mother-and-father.htmyou're welcome!
Arden.
Arden was the maiden name of Wm. Shakespeare's mother.
The Coram hamlets are not a thing but rather a collection of locations, hamlets in this case, which share the same name. Coran is a relatively popular name and hamlets of that name have been noted in the united states, great Britain, and northern France.
The Ardens were Shakespeare's mother's family; her maiden name was Mary Arden.
Mary Arden, or after her marriage, Mary Shakespeare.
Claudius