The 1918 Catholic Encyclopedia article on Patron Saints provides an overview of how a Patron was chosen for a church, a city, a country, and a trade/profession. The bulk of the article focuses on how a Patron Saint was chosen for a church: the origin of the practice, and the criteria for the choice, and practices in various regions (Rome, England, Scotland, Ireland, Continental Europe, United States, Canada, Australia, British South Africa). On choosing a patron of trades and professions:
The whole social life of the Catholic world before the Reformation was animated with the idea of protection from the citizens of heaven. It has been stated that in England there existed 40,000 religious corporations, including ecclesiastical bodies of all kinds, monasteries and convents, military orders, industrial and professional guilds, and charitable institutions, each of which had its patron, its rites, funds, and methods of assistance. Some idea of the vastness of the subject may be gathered from a few examples of the trades under their respective patrons: Anastasia (weavers), Andrew (fishermen), Anne (houseworkers and cabinet-makers), ... These patrons with very many others were chosen on account of some real correspondence between the patron and the object of patronage, or by reason of some play on words, or as a matter of individual piety. Thus, while the great special patrons had their clients all over Christendom, other patrons in regard of the same class of objects might vary with different times and places.
The 2002 New Catholic Encyclopedia entry on Patron Saints has an extensive A-Z list of patron saints from Academics (Thomas Aquinas) to Wine merchants and Bar keepers (Amand of Maestricht). About how they are chosen:
The choice of heavenly patrons by guilds of artisans and craftsmen was dictated by some attribute or legend associated with the name of saint that linked their members to him or her. St. Vitus who was said to have been martyred in a caldron appealed to kettle-makers. Archers venerated St. Sebastian. Wagon-makers chose St. Catherine of Alexandria because a wheel was the means of her martyrdom. Tailors sought the patronage of St. Martin of Tours because he was said to have cut his mantle in half, giving one part to a beggar who turned out to be Christ. The intercession of other saints was implored for particular illnesses because they themselves had suffered from a particular malady or they ministered to those who had.
A 2012 parish article Patron Saints by RCIA director Tom Schenk provides a short summary (emphasis mine):
The earliest records show that people and churches were named after apostles and martyrs as early as the fourth century. Recently, the popes have named patron saints but patrons can be chosen by other individuals or groups as well. Patron saints are often chosen today because an interest, talent, or event in their lives overlaps with the special area.
Angels can also be named as patron saints. A patron saint can help us when we follow the example of that saint’s life and when we ask for that saint’s intercessory prayers to God. For example, Francis of Assisi loved nature and so he is patron of ecologists.
Francis de Sales was a writer and so he is patron of journalists and writers. Clare of Assisi was named patron of television because one Christmas when she was too ill to leave her bed she saw and heard Christmas Mass—even though it was taking place miles away.