A group of work friends and I have been playing the through Dragon Heist campaign for a couple weeks now, and we are starting to get to where I as a DM can start incorporating little hints to character backstory during game time.  Whenever I DM a game, I work with the players as much as I can on creating complex characters with a rich backstory aching for the campaign to explore it further.  While working with one my players on creating their backstory, we created some interesting interwoven connections with the NPCs for the campaign.  For example, her father is Davil Starsong.  While we were creating these connections, she gave out an idea where her parents are betraying each other to try to keep my player's character on their side in her parents' interesting relationship.  However, all this back and forth was to remain secret to her character, it will later be discovered by her in the game.  Although this will remain secret for the rest of the players and will be a surprise when all this comes out, allowing genuine shock and betrayal, she knows this whole time and will not get the same feeling.  This led me to a brainstorming session with myself of other things I could do to attempt to create that same feeling for her.  But I do not know if messing with her backstory or adding secret things about the people close to her is taboo and should be left alone sort of speak.  So I pose this questions to you guys, Is it okay to create people in a character's backstory that the player wouldn't know.  Or at least secrets for backstory NPCs that only I as a DM know. 

Obviously the potential payoff for this still has a ways to go but I would like to start planning this stuff now so I can have these secrets working in the background.  Thanks in advance for the help and I look forward to the discussion.

It would very much depend on the player's comfort level with you as a DM, and if the secret is something that isn't too uncomfortable for the player personally.

You can always ask, which seems a little counter-intuitive, but can actually work well.  Basically, tell the player exactly what you just posted. . . you love the idea of those genuine feelings of shock everyone else is going to get when this comes out, and wanted your in-the-know player to experience that, as well.  So are they okay with you creating something in their character's backstory unknown to the player?  Knowing that there's a secret is still a world away from knowing what that secret is, so if they're cool with it, you may proceed.  If the idea makes them uncomfortable, you can back off.