Accidentally Correct Writing: There actually is a Greek deity named Kratos, the personification of strength. The original creators were not aware of him until after they had settled on naming their character Kratos after the Greek word for strength, kratos.
Just take a look at the character sheet. Practically every character to appear in more than one game has had this happen at some point or another. Part of it can be attributed to the fact that all of the gods were completely redesigned between the first and second game, other times it's just good old-fashioned recasting.
Among many other format changes, it finally happened to Kratos himself when the series moved from the Greek Era to the Norse Era. Motion capture had become ubiquitous in video games by this point, and Terrence C. Carson, who voiced Kratos throughout the Greek Era, would not have been up to the task of portraying Kratos physically as well as vocally, so he was replaced with Christopher Judge. Many dubs of the series followed suit and recast Norse-era Kratos as well.
Self-Deprecation: Meta-example. Series creator David Jaffe has stated that he finds the games' combat to be shallow compared to other games in the genre, and that he would have made the series a little differently if it were a new IP today. Possibly downplayed, since he never expressed explicit dissatisfaction with the mechanics, and even went on record to bluntly say he is not decrying the games themselves.