I don't remember much about this manga so it will be brief. The manga starts out with the main character and several other characters who are deemed heroes for defeating the demon king I believe are now given titles. The title if I remember correctly fire emperor, water emperor, etc., etc. Our main character is bestowed with the title lighting emperor from there the story goes into his reincarnation. His reincarnation is from the same family but his reincarnation is weak and his family looks down upon that. He gets upset that his family is using his name before reincarnation to oppress their own kin.
I believe this is The Unsuccessful Yet Academically Unparalleled Sage ~A Cheating S-Rank Sorcerer's Post-Rebirth Adventurer Log~, also the answer to this question.
The main character is called the Thunder Emperor. He was one of the most powerful mages in the country. He and the other powerful mages were given the title of X Emperor, where X was the magic they were strongest with. Towards the end of his life, one of the other mages figures out a way to determine magic compatibility. He tests himself and finds out he has no compatibility with any magic. When he dies, he is reincarnated as one of his descendants. Once he remembers his past life, he tests tests out his magic. He then finds out his magic is as powerful as it was in his previous life, despite still having no compatibility.
His father is a powerful sorcerer who is never around and has another woman as his wife, along with 9 other concubines. The main character lives in the country with his mother. The two of them both lack compatibility with magic, and are looked down upon.