^Title Haven't come across any like this yet funnily enough considering the numerous amount of stories with reincarnation as the basis (of course haven't read all that's out there, but read a fair few).
Realms In The Firmament It's funny to see how is everyone praising him nonstop (the person he was in his past life) while he is laughing secretly (That's me!) Spoiler About when did he reveals his true origins, i'm not too sure since i've read it on a spoiler, 900+ (maybe?) his family has some troubles but he solves them because he revealed his identity to someone from his past life.
Mushoku Tensei No Fatigue At least these two. Few others come to mind but I can't remember the names.
The Death Mage who doesn't want a fourth time. Everyone on his inner circle knows that he reincarnated from earth and even the beefs he has with differents GODS.
Nagai Koto kinda has this. It's a ways into the story (had to read mtl far beyond the current translation) before he finally tells his waifus. But when ever he meets people who he knew in his past life, he's pretty forthcoming with who he was.
The ones I know are already mentioned. Also, while no family is involved since reincarnators just pop out with a new body grown up to their previous age, Because I Reincarnated as a Succubus, I’ll Squeeze Out Milk. Perhaps Souen no Historia has eventually something like that, but given that both WN and translation are stalled, we'll probably never know.