What is Juliet's father's first name in Romeo and Juliet? Also, what are Romeo's mother's and father's names and Juliet's mother's name?

We do not know the first name of Juliet's father in Shakespeare's play Romeo and Juliet. We know him as Lord Capulet, and Capulet is his surname. It is also often used to refer to the whole Capulet family.

Juliet is a Capulet, whereas Romeo, whom she falls in love with at first sight, is a Montague (he belongs to the family of Montague). The play's setting is Verona, Italy. These two families hate one another; there is an ongoing feud between them. 

Just as Juliet's parents are referred to as Lord Capulet and Lady Capulet, Romeo's parents are referred to as Lord Montague and Lady Montague. 

It is not strange that their first names are not given in the play. During this time period (Romeo and Juliet was written around 1594), people of the upper class were not usually referred to by their first name. Out of respect, it was customary to refer to people by their surnames with their status or position stated first. Romeo and Juliet are referred to by first name probably because they are very young and don't have a specific status yet. Juliet is only 13 years old in the story.