You can use computer software to make new style files for the DGX-620, but you can't make them on the DGX-620 itself.
There are a number of programs which let you create new style files, either from scratch or by using parts of a MIDI song file.
Jørgen Sørensen has a lot of free utilities at his site (http://www.jososoft.dk/) for working on or creating MIDI song files and Yamaha style files. I recommend his utilities for their diverse functionalities and ease of use. He takes the approach of writing small utilities that perform specific functions, rather than large programs that perform many functions.
You can create as many style files as you wish, but I think there might be a limit to how many you can store in a directory on a USB flash drive and still have the keyboard be able to see all of the files in that directory. If there is, I'm not sure how many it might be, but I think I've seen references in some Yamaha manuals to no more than 250 song files in a given folder.
However, you can't play style files directly off of the USB flash drive the way you can with song files. Instead, you must "load" a style file from the USB flash drive into the keyboard's system memory, which is called "registering" the style file. From what you asked about User Styles 31 through 35, it sounds like you can load up to 5 style files into the keyboard's system memory.
If you want to use additional style files, you'll need to load them as needed. For example, you could load 5 style files into numbers 31 through 35, then later load 5 different style files into numbers 31 through 35, and so on.
There isn't a program that is specifically for making styles for the DGX-620. Rather, there are programs that can be used for making style files that could be used with Yamaha keyboards in general.
To be honest, trying to create style files of your own can be difficult to learn and time-consuming to master, so it is often better-- and certainly simpler-- to use style files that other people have made, and then tweak them for your particular model of keyboard if necessary. You may wish to check the following pages for style files to try: