There are a few different approaches one could take in choosing a patron saint for yourself.
You could choose a saint by what is your profession, need, desire (devotion) or name's day.
A name day is a tradition in some countries in Europe, Latin America, and Roman Catholic and Eastern Orthodox countries in general. It consists of celebrating a day of the year that is associated with one's given name. The celebration is similar to a birthday.
The custom originated with the Christian calendar of saints: believers named after a saint would celebrate that saint's feast day, or in the Eastern Orthodox tradition, the day of a saint's death. Name days have greater resonance in the Catholic and Orthodox parts of Europe. - Name Day [Saint] (Wikipedia)]1
A patron saint in the Orthodox Church is regarded as the intercessor and advocate in heaven of a nation, place, craft, activity, class, or person. Since the time of the early Christians up to the present, a vast number of patron saints have been recorded.
Christians have long chosen the names of Saints to proclaim their link with their spiritual family, the Church. The name may be of a Saint commemorated on or near to the day of the child's birth, or for whom the family has a special devotion. Likewise, an adult received into the Orthodox Church chooses a Saint's name to whom he/she has a strong attachment. In days past, this was often a costly witness for believers living in a non-Christian society, as their very names (Nicholas or George, Elias or Barbara) labeled them as Christians.
Each day of the year, the Church honors a number of Saints. The day the Church honors one’s Saint is one's "Name Day," an occasion to honor the memory of the Saint whose name we bear, and to give thanks for his/her daily intercession on our behalf. Individuals whose names are not found on the Calendar of Saints celebrate on All Saints Day, the Sunday after Pentecost.
We are to pray and have a special devotion to our Patron Saint. His or her life should be read and studied so that we learn how our lives should be directed. Our Patron Saint becomes a true hero/heroine for us to emulate. - Celebrating Our Patron Saint's Day
A list of Orthodox saints and their feast days may be perused at the following sites: