Solidus Snake official action figure by Square Enix Play Arts Kai (description identifies the swords as Minshuto and Kyowato; only official evidence I could easily find of this being their names):
https://www.amiami.com/eng/detail/?gcode=FIG-IPN-4453&page=top

Forum post from 2006 claiming they are named in concept art in The Document of Metal Gear Solid 2:
https://mgsforums.com/solidus-39-s-blades-t17836.html

The Art of Metal Gear Solid 2: Sons of Liberty (pages with Solidus: 80-82, 149-150):
https://archive.org/details/the-art-of-metal-gear-solid-2-sons-of-liberty/Art_of_MGS2-0078.jpg
https://archive.org/details/the-art-of-metal-gear-solid-2-sons-of-liberty/Art_of_MGS2-0145.jpg

The Document of Metal Gear Solid 2 (supposedly in this game but cannot find evidence):
https://www.youtube.com/watch?v=58M4hTpj6k8#t=928

Sword names article:
https://screenrant.com/metal-gear-solid-2-solidus-snake-sword-names/