Well, he could wear a hood and mask if he wanted to, but I don't think the Church would care that he's Omestri, as long as they have no reason to think that he's harboring "heretical" thoughts when it comes to his devotion to Varya. In fact, I think they would actually consider it a victory and a source of pride that they were able to "break" an Omestri slave into "loving" Lord Varya. Like every other child who enters the Seminary, your character has been brainwashed into worshipping the Ravenous Lord, and the Church believes they succeeded in that, But deep down, your character will feel what he feels and believes what he believes. It depends on how crafty he is, but he would probably never let his inward feelings show to anyone else, as it could possibly mean death. The only people he would probably share his true feelings with are those who share the same, but only in like, super secret situations. 

As far as him hiding being an Omestri because of the hatred and disgust that Varyans feel for that race-- it would depend on what kind of person he is. Would he want to hide his origins to avoid unwanted attention, or would he have a proud and fuck-you-guys-i-am-what-i-am attitude towards it? It really depends on that, I think.