In general, no matter how you look at it (either the truth that Syrus knows or the lie he puts on as a spy infiltrating Civitas), he can't deny he has been raised for the last year-ish to be a tool for the gods. He isn't quite as biter about that as the act he puts on for the other BC members, but he'd be lying if he said the last year was all puppies and rainbows. Thanks to Elena and Rowan, older demigod couple that lives away from camp, who helped train Syrus in secret, gave him some semblance of a normal life when he wasn't training. He grew to really appreciate and care for them in a short time, and that rubbed off on his personality.
To sum him up he is the epitome of there being a time for everything. He can have goofy laid back moments, but he is also responsible and punctual. If he says he'll do something, you can guarantee it will be done, done well and done on time. He hasn't dated much, but is open minded and most likely pansexual. Because he didn't have anything closely resembling a normal childhood, even for demigod standards, he sometimes wonders what life would have been liked if he'd been raised from birth (the long way) by Elena and Rowan. Maybe he would have had a pet kitten, been taught to play the piano or mix a simple love potion by his mom, maybe taught to use a bow and ride a bike by his dad. He tries not to dwell too much on it though, and only opens up about that kinda stuff to his closest friends.
In spring of 2013, Skylar Lune and a bunch of his friends went partying one weekend in Las Vegas. Long story short, Skylar unknowingly hooked up with Psyche, his father's wife. Eros wasn't happy about this, and was even less happy about this when he found out Psyche was pregnant with Skylar's child. When Syrus was born, they weren't really sure what to do with him. Psyche knew Skylar was in no condition to raise a child, he could barely take care of himself properly with all the partying and drinking. Psyche knew she couldn't raise him but what could be done. A few of the gods proposed using the child, they could accelerate his growth and use him to infiltrate the Broken Covenant. There had been debates for months that the Civitas faction had the most reasonable demands, and that perhaps getting some off their own people on the inside, loyal to them, they could eventually convince Civitas to turn against the others.
So they aged him to nearly 18 years old and worked towards training and raising him (Psyche at this point was no longer involved). For a few months each god helped Syrus learn something. Mnemosyne taught him language, Hermes taught him about the world, Ares taught him about fighting, etc. Then they sent him to train secretly with two demigod adults in secret, Rowan and Elena. So for ten months he lived with them where they taught him to fight monsters and use his powers. Then it was time to join the BC and with Kina Moriales already in the BC getting in was easier.
History the Gods Told Him
The gods didn't want him to know how his real father was, especially Eros who was deeply hoping that it would cause Skylar problems one day, to further get back at him for sleeping with Psyche, and the way everything had played out so far, it was looking like he might get some revenge without having to do any direct interference to Skylar himself.
The gods told him a story about how the biological father died in a monster attack before he was born, and that Psyche had originally thought that she would have to leave Syrus with an adoption agency, until the other gods got together and hatched the plan to age him and use him as a spy.
History He Told the BC
Because he needed a better story to tell the BC, as the truth would give him away as a spy, the gods helped him come up with a believable back story, with the help of Elena and Rowan. Elena being roughly "6" years older than Syrus, the story is that she is his half sister on the mortal side. That her father had an affair with Psyche when Elena was a little girl. The father never liked him as much as he loved his oldest daughter, and often called him "the mistake". That led to quite a complex as he grew up and he was always very envious of his Sister, though he never truly hated her for it.
Watching his sister go through some of the problems she did, made him dislike camp and the gods. She was pregnant and going to elope with Rowan around the time that Syrus should have been going to camp himself, but he chose to live with his sister and try to help her protect the baby, while her and her demigod husband Rowan trained him to fight monsters. After a horrible incident where their baby was kidnapped, all because of petty problems with the gods, he grew to hate their stupid rules even more. He hated that they couldn't just have normal lives, they didn't ask to be born a demigod with powers and monsters hunting them, and they weren't even allowed to have any direct help from their parents. This all led him to join the BC, specifically the Civitas faction, feeling that not all the gods were bad per se, but the rules they had and lives they forced upon their children were totally unfair and that something needed to change.