No. There are thousands of saints, so it would be impossible for every single one of them to have their own feast day (unless we decided to devote each day of the calendar to several different saints). Instead, only those saints who had the greatest impact on the Church or around whom a fervent devotion has grown are celebrated with feast days in the liturgical calendar.
All known and named saints have a feast day. On any day of the week there may be 20 or more saints who are memorialized. Go to this link for a clickable calendar to see what saints have a feast on any particular day of the year. For those unknown saints without a feast day, they are celebrated on All Saints Day, November 1, each year.
Every known saint is assigned a feast day. The feast of Saint Patrick is March 17 which some believe is the day of his death.
The feast of Saint Elizabeth is November 5.
The feast day of Saint Juan Diego in on December 9.
Pope Benedict I is not a saint and has no feast day.
Saint Maria Goretti's Feast Day is July 6th.
The feast day of saint Mark is April 25.
Saint Laura's Feast Day is October the 19th.
Saint Helena's feast day is August 18.
The 23rd of April is the feast day of Saint George.
Saint Christopher's feast day is July 25th.
July 24 is the feast day of Saint Charbel.
August 11 is the feast day of Saint Philomena.