Today is the feast of Queen St. Catherine of Alexandria, Virgin and Great Martyr, who as a sort of personification of Christian Alexandria is the patron saint of philosophers. Her list of recognized patronage is in fact immense, and a good example of how saint-patronage works.
Her basic story has three elements: her legend involves her defending the Christian faith in argument against the best pagan philosophers of Alexandria, she is a Virgin Martyr, and they first attempted to kill her by breaking on the wheel but instead the wheel broke. These make her respectively the patron saint of philosophers, a patron saint of maidens, and the patron saint of anyone who makes a living off a wheel.
Patroness of Philosophers. St. Catherine was one of the most popular saints of the Middle Ages, both East and West, and her association with philosophers made her particularly favorite patron of intellectuals of all types. Her name was often associated with monasteries that had a particular reputation for study, and in the West, St. Catherine's Day was a major celebration in the universities. Because of this, she became patron saint not just of philosophers but theologians, orators, jurists, students (especially but not exclusively female students), archivists, librarians, lawyers, preachers, as well as the University of Paris and a number of other colleges and universities.
In addition, her association with study often results in her represented with writing implements in iconography, and thus as a further derivation, she becomes patroness of those who earn their living by writing: secretaries, scribes, stenographers, clerks.
Patroness of Maidens. As a popular saint who died as a virgin martyr, she is often invoked for girls and unmarried women, especially (but not exclusively) those involved in studies. This was probably her second most popular patronage, but it has had particular durability; there are a number of countries that still celebrate St. Catherine's Day as a special day for young unmarried women. A further derivation makes her patron saint of spinsters (perhaps strengthened by the occasional association of spinsters with the spinning wheel).
Patroness of the Wheel. Breaking on the wheel is a horrible torture; it's basically beating someone to death with hammers. The reason it's done on a wheel is that if you stretch someone out on a flat surface and try to beat them to death with hammers, it's actually much harder than it sounds. To be really effective, you need to splinter bones, but it's hard to splinter bones that are supported by a flat surface. So ancient torturers came up with the expedient of stretching someone over a wagon wheel -- a strong surface that distributes the force of the hammer, but which has lots of holes, so that wherever the hammer hits over a gap, the bones snap. The fact that the human race ever learned this is a tribute both to our extraordinary ingenuity in learning and our depravity. According to the legend, they tried to break her on the wheel, but the wheel shattered instead -- which, I think, when you consider how breaking on the wheel works, is an obvious miracle. So she was actually beheaded, but her status as the Wheelbreaker looms large in the imagination, and the broken wheel is a very recognizable sign of St. Catherine in iconography, so she became the patron of everyone who works with a wheel: potter, spinner, wheelwright, miller, milliner, knife sharpener.
The custom of having patron saints historically grows out of the custom of having titular saints for churches. Churches were originally built in locations associated with martyrs or other saints, to such an extent that when churches had to be built elsewhere, they were also given titular saints, which is why Catholics and Orthodox and some Protestants name their churches (and other religious buildings, like monasteries) as they do. This then meant, however, that people in an area around a church, particularly a very important one, would tend to share, as a community, devotion to that saint, recognizing the saint both in liturgy and in popular piety. Thus titular saints of churches became patron saints of towns and cities and regions. Patronage of professions grew out of this, but as far as I can tell it is unclear whether professional patronage originally did so directly from territorial patronage as an extension of participation of guilds in popular regional celebrations, or if it did so from popular patronage.
Saints, of course, are depicted in icons; in order to facilitate recognition, they are given identifiers, usually known as iconographical attributes, like St. Catherine's Wheel. Icons are used in prayer, and it's not surprising, given how human imagination works, that people tended to pray to or celebrate the feasts of saints whose attributes were somehow associated in their minds with what they were praying about or celebrating. Common legends about the saints would have a similar effect on the imagination in prayer, as would sharing a name or even an approximate name with a saint. We are connected to some of our forebears only by legend, and to some of them only by having their name; but both legend and enduring name are forms of memory as much as history is, and both thus play an essential role in commemoration and praying with the saints. Traditional popular saint-patronage thus marks out what people have prayed about on a large scale for a long time. One can well imagine a potter long ago going into a church, worried about something to do with his profession, and gravitating immediately to the saint with the wheel, or medieval guilds of wheelwrights, needing a way to participate in their community as part of their functioning as guilds, obviously celebrating the saint that would allow them to do something with wheels in their celebration. This is, of course, what basically happened in the universities: philosophy was the heart of the medieval university, so obviously people celebrated a saint so clearly associated with philosophical argument. One can also imagine a reverse process, in which people are already celebrating a saint's feast for some other reason, and the way in which they do this is affected by attributes, legends, and the like.
Saints who are extremely popular, like St. Catherine historically, thus tend to collect a lot of patronage, a mark of their role in the prayer and piety of the Church through time; they have titular patronages, territorial patronages, professional patronages, and popular patronages, all.
