Obscure early-PS1 FPS, Kileak: The Blood (Kileak: The DNA Imperative), had a just-as-obscure sequel; in Japan, it retained the "Kileak: The Blood" title, but in the US, it was renamed to "Epidemic." There is also a third game with very similar designs, though seemingly no explicit connection to the former two; BRAHMA Force: The Assault on Beltlogger 9.
Dynamix's Apple II-era Battlezone clone, Stellar 7, eventually received a sequel (after its IBM PC-based remake proved popular enough for one); its title was Nova 9: The Return of Gir Draxon. Not long after, another game in the series reached Sega CD, Stellar Fire. It's slightly unclear why the rename; Stellar 7 retained its original title through a second remake for 3DO: Stellar 7: Draxon's Revenge.
Another Dynamix game, the RPG Betrayal at Krondor, had a sequel in the works, but Dynamix were unable to retain the license to author Raymond Feist's book series at the time, so the sequel wound up being set in a completely different universe and received the title Betrayal in Antara. It retains much of the game design from its predecessor.
These are arguably not "sequels," but the genealogy is solid enough that I consider them fairly related. Origin's space sim Wing Commander had a number of spinoffs, both in-universe and out. Wing Commander: Privateer was originally known as Trade Commander during development, but was renamed presumably for marketing purposes. Though that naming convention stuck for Strike Commander, the Top Gun-influenced real-world flight sim from the same dev team. Further along that genealogy, the dev team borrowed the Strike Commander engine and one of the title's words for a World War 2 flight sim, Pacific Strike, and ultimately concluded that bloodline with Wings of Glory, another game on that engine that is set in World War 1. Though, curiously, Pacific Strike had one other pseudo-offspring; the PlayStation 1 game Zero Pilot: Ginyoku no Senshi is, in fact, an elaborate port of Pacific Strike, retaining the flight model and many of the Pacific Strike assets, but redoing the entire campaign mode to be set from a Japanese perspective.