What you're talking about are the system names, which are only very loosely linked to the star types. The OP is talking about what appears when you click on a system in the Galaxy map and then click on the Info tab, which is currently the only place to see the star class.
For example, let's have a look at a system out in procedurally-generated space: WREDGUIA TM-G c25-4. The star class listed for that system is K0 VZ. You'll notice the "K" isn't directly indicated anywhere in the system name. The spectral class is essentially the star's colour: "K" is "orange". So this system's star is a large (0) orange (K) dwarf (Vz).
This thread has considerable discussion about breaking down and analysing the meaning of the procedurally-generated system names, and what all those letters and numbers actually mean. But in brief summary, the "loose linking" I mentioned between star types and the system name can be seen in the last letter in the system name, the lowercase letter before the string of numbers. That letter is called the "mass code". It essentially determines the approximate mass of the star. The mass code ranges from "a" (smallest) to "h" (largest). Mass code h stars are almost always black holes, Wolf-rayets, or large bright O-class stars. Mass code "d" contains your medium-sized, A and F class stars, as well as neutron stars. Mass code "a" contains just tiny brown dwarfs.
In the system I mentioned above,m the mass code is "c". This is a code for stars which are at the smaller end of the spectrum, ranging from stars about the size of Sol down to small class M red dwarfs. So in mass code "c" systems, you're likely to find the occasional smaller G type star, lots of K type stars, and a few larger M type stars, perhaps the occasional White Dwarf if you're in a white dwarf belt, and not much else.
The numbers that come after the mass code are essentially the "catalogue number" for the star - the number of stars in that subsector with that mass-code. In this case, "c25-4". The "25" actually indicates how far North into Wredguia Sector this particular subsector "TM-G c" is; there are 32768 mass code "c" subsectors in Wredguia Sector and only 17368 possible three-letter combinations, so they've needed to use "TM-G c" at least twice. The last number after the hyphen, "4", indicates that this is the fourth star in the TM-G c25 boxel.
If you want to sort your destinations by star type, ignore the system name, and switch the galaxy map filter to "star class" mode, then deselect all the star types you don't want to visit. Many beginner explorers deselect everything except the scoopables (OBAFGKM), but flying with that set selected will give you a small, boring M-class red dwarf more than half of the time. Experienced planet-hunters will narrow the focus more. Personally, when travelling from place to place I almost always fly with just A, F and G selected, as well as the weird stuff like non-sequence, carbon stars and Wolf-Rayets.