First i was thinking why has she not been mentioned, and how did Garp even get Luffy under his care. Luffy didn’t even know he had a father and as of yet no one questioned him on his mother either Garp has not said anything either as if its someone higher up said not to. Something of the utmost secrecy.
My theory is that Luffy’s mom is a Celestial Dragon. I think that through some weird fate Dragon encountered her and they fell in love. They had a forbidden child and the Tenryūbito killed her for laying with a commoner and worse a member of the D. tribe, so Dragon barely escaped with Luffy.
The World Government or even a select few of the highest rankings knew of this betrayal of one of the Tenryūbito and learnt that the new born baby was entrusted to Garp. They ordered him to keep Luffy a secret and never reveal what blood flows through his veins. This could also lead back to why Garp has Luffy growing up in east blue, in a place where no one really cared about.
*Theory by Funnelingyourtunnel