Finn is the enlisted Stormtrooper who became a central figure in the Star Wars sequel trilogy. The only thing we know is that after Palpatine was killed at the end of Return of the Jedi, the clone factory on Kamino was closed down. As the Kaminons stopped producing clones, The First Order had to replenish their soldiers so they took youngers and enlisted them and make them the new troopers.
On his first mission on the desert planet of Jakku, he saw his fellow Stormtroopers get killed, the shock of which caused him to re-evaluate everything he stood for. After evaluating, he decided to rescue Poe Dameron and join the resistance.
It wasn't easy and straight forward as that, first he came across Rey and he wanted to be her guardian. Then he found Han Solo after Finn and Rey stole the Millennium Falcon from a trader on Jakku. Han Solo was able to put him in touch with the resistance on Takodana .
Finn has walked out on the First Order and he's twice tried to walk out on the Resistance. The first time he tried to walk out on the Resistance was on Takodana when he was going to get a lift to the Outer Rim. The second time was when he woke up on the resistance medical craft and was going to use an escape pod before being caught by Rose Tico and being stunned.
Rey seemed to want to know who her parents are, she tried to find out when she jumped into a cavern on Ahch-to but to no avail. Finn doesn't seem to be interested in who his parents are and they aren't mentioned. There are a few suspects to who his father could be none as to who his mother is. Am only interested in canon characters so if I missed anyone, let me know.
We know that Lando Calrissian is coming back for the third and final movie of the sequel trilogy. Where he has been for the first two is unknown. If Lando is the father, he could have been looking for his son during the events of the first two films.
The last we saw of him was being thrown out of the window by Palpatine back on Coruscant . If Darth Maul could come back alive after being sawn in two by Obi-Wan Kenobi's light saber then there's always a possibility that Mace Windu was able to survive what happened to him. Mace could have got amnesia and settled down with a woman without knowing he was able to control the Force. He would have had to have lived a long time and been able to still be a dad to be Finn's son.
If we do find out who the parents of Finn are, they'll probably be a new character, not someone we've already met. There doesn't seem that much interest in knowing his parentage, all family questions are around Rey.
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