I have a general idea of the differences of roles between pre-Renaissance and Renaissance artists; however, I'm hoping that my knowledge can be expanded on. At what point did artists go from being commissioned by the Church only and rarely being given credit by name to being commissioned by patrons, achieving fame and being able to create art in whatever subject they wanted? What factors influenced this change?
I wouldn't say that, even by the High Renaissance, artists had that much freedom over their subject matter. It was still very much a matter of the patron's (whether it be royalty, church, or private) will. The more well-known artists had a bit more input (I'm thinking, for example, of Titian and his portraits for the Spanish kings), and certainly more freedom to choose and be exposed to a wider range of possible patrons, but they weren't truly able to just paint for the sake of it - that shift was still another couple of hundred years away. Everything had to be created for a purpose.
In terms of patronage, the addition of private citizens (usually middle and upper class) as patrons to the standard patronage of church and royalty coincided with the rise and growing wealth of those classes. You have to remember that at this point, art museums - and publicly accessible art in general - weren't concepts. Art, for a private citizen, was a status symbol: something that the church and royals had had for centuries, that now they could too. The growth of private collecting & commissions also benefitted the artist because citizens tended to have more wide-ranging tastes than the royals or especially the church, based both on personal taste and current fashion, thus giving the artist a bigger scope in which to work, as well as another means of making money.
The financial aspect of private patronage is one reason that it really flourished in Italy and the North - in a country like Spain, for instance, the financial gap between the royals and their subjects was so wide that there was barely a middle class, let alone one with the disposable income to spend on art.
So I'd argue that it wasn't really that the role of the artist changed all that much; rather, the perception of the artist in society, and the function and purpose of art itself, that benefited most from Renaissance ideals during the period - he was gradually elevated from a craftsman to a serious and in-demand professional, who had access to an ever-growing pool of patrons and ideas than his predecessors.
I really recommend Jay Levenson's Circa 1492: Art in the Age of Exploration as a starting point if you're interested in this subject / period. Ann Harris also has a really interesting text on the same topic, but it deals with the period just after the Renaissance.