So Georgian and Victorian as descriptors refer to a particular era or style, not to the monarchy. Each monarchical line is referred to by the name of their houses. George I, II, III, IV, William IV, and Victoria are all from the house of Hanover, and are collectively known as Hanoverian. The Stuarts were all from the Scottish house of Stuart, and are referred to as the Stuart kings.

Georgian and Victorian are not used to describe the monarchy, but are instead used to describe things like building styles, clothing styles, furniture styles, etc. that were popular during the rules of Queen Victoria and the George's. Kings George I-IV ruled consecutively for over 100 years, and Queen Victoria ruled for nearly 70 years. The longest reigns of the Stuart Kings were around 30 years, and they alternated names between James and Charles. So no Stuart king reigned long enough to have their period named after them like Victoria, and they lacked a common name, so their reigns couldn't be lumped together like the Kings George were.

With many things in choosing the English Language we use, it's complex. There is no single or final list of reasons, but we can point to three key components (in no particular order): General Linguistics, Cultural Pride, and time duration.

First off (again, not in order of import) is General linguistics or just how the names sound. Stuart sounds nice and clean, easy to say unlike their first names when converted to proper adjectives - Jamesian and Carolingian. It would even be difficult to get people agree on the proper adjective for Charles. You have the opposite problem for George / Victoria. Comparing Georgian to Hanoverian you have three syllables to five syllables (? history person, not grammarian). Not a big deal, but it really comes into play when you compare Victorian to Saxe-Coburg-Saalfeldian (not even going to try and count syllables; See note at bottom). Her Grandson started using the name "Windsor" as well, but Windsorian just rolls off the tounge oddly.

Next up, is cultural pride. Hanover and Saxe-Coburg-Saalfeld are both German names. The fact that German families came to rule the throne of England was not always well received. And German - British relations in the early 20th Century did not improve. This leads to the use of the more "British" Georgian and Victorian. (Note: In historical discussions, Georgian / Hanoverian are used semi-interchangeably).

Finally, are the time periods involved. A theoretical Jamesian period would be one 22 year period and then a second three year window sixty years later. These descriptors would then be small, and confusing if we were talking about the first / second period and unlikely to differ from surrounding periods. It is just easier and generally more accurate to talk about the ~111 year reign of the entire dynasty. Contrast this against the Victorian era which is 64 years in one reign alone. And in this case if we were to expand it to the Saxe... / Windsor era we'd have 180 years and counting. A period covering the invention of Morse code to Reddit (sorry 20 year rule). A last name descriptor that large loses its usefulness too. Which technology level are you talking about?

Note: Some genealogies will place Victoria in the house of Saxe-Coburg and Gotha after her marriage. German nobility naming rules is outside my scope, but the Saxe-Coburg-Gothian period would maintain all the same arguments.