Chiss names are indeed complicated, being constructed from three parts. For the case of Mitth’raw’nurodo, the “Mitth” is the family name (like a surname for us), “raw” is his given name, and then “nuruodo” reflects his relationship to his family. Thrawn was not born into the Mitth family by blood, he was adopted into it, and so he was originally known as Kivu’raw’nuru, since his birth family was the Kivu.
Following his adoption into the Mitth his name changed to Mitth’raw’nuru, and he was known as such in his early military career. However, later the "nuru" termination seems to have changed to "nurodo" with no explanation. A Del Ray editor has tweeted:
The "odo" has a currently unexplained special meaning, and is not part
of his Mitth family name. So the scenes when his name ends in "uru"
are before he's earned those 3 letters. As for what exactly those 3
letters mean that's something Tim plans to explore. Stay tuned :)
That tweet was made on September 5th 2020, and as far as I know (though I'd love to be corrected!) the hidden meaning has not been revealed yet.