It's not clear from the script. But that might be a good directorial choice--it would make her suicide even more horrific and her pleas to be let in on what is going on even more poignant.
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She is the daughter of Marcus Porcius Cato, and more importantly for the play, she is Mrs. Brutus.
Portia was Brutus's wife in Julius Caesar. Later in the play, she kills herself because Brutus fled Rome. It's quite pathetic actually.
Well there's Caesar like Julius Caesar, Cinna like Cinna the poet or on of the conspirators who killed Caesar, Octavia from Shakespeare's Julius Caesar, Cato like Cato the elder, there's also a Brutus and Portia form Julius Caesar play.
Technically Since she is Married To Marcus Brutus, Her last name would Be Brutus The Roman women retained their own names upon marriage. Brutus' wife Portia was Portia Catonis. She was the daughter of Cato the Younger.
The most important character in Julius Caesar is not Julius Caesar, but it is Marcus Brutus. The reason why Shakespeare put Julius Cesar as the title is simply because it was more appropriate. It is the killing of Julius Caesar, which supplies the motive for the play. The death of Julius Caesar takes place before the middle of the play, however, his spirit dominates the entire work. It is the spirit of Julius Caesar, alive or dead, that supplies the struggle for Brutus and fellow conspirators.