Kaga: A region of Japan
Akagi: A mountain in Japan (perhaps familiar to fans of Initial D)
Souryuu: lit. "Blue Dragon"
Hiryuu: lit. "Flying Dragon" -- really a modified Souryuu, named with the "dragon" (ryuu) suffix to show the relation to the Souryuu class.
The JMSDF also maintains several traditions from the Imperial Navy, such as the songs, ensigns, and technical terminology. One of the most well-known traditions that's been maintained across the two navies is the Japanese curry lunch served every Friday (there are even ads on trains for it as a tourist attraction).
IIRC the current naming system was also inherited from the Japanese navy, if you were curious about why two of the ships you named are named after places. Wikipedia has some more information on that: https://en.wikipedia.org/wiki/Japan_Maritime_Self-Defense_Fo...
Kaga and Akagi are classes of ships so there is and wil be a bunch of them. Hiryu and Soryu were specific ships, hopefully these names stay with them.
It’s “funny” how all the army ship games and manga