Well Dan had some (presumably) good reasons for not wanting to show his clan symbol and wings, now he has a few more.
We also know there is at least one person at the party who knows he is of Cyra clan and may blab his secret, but I imagine she can be persuaded by simply saying "Don't say anything about who I am and I won't round up my adventuring buddies to take you out", heck promising to not murder her on the spot might do it.
It is probably common knowledge at SAIA right now that he is a Cyra child.
It is inevitable that some gossip has reached those that attend the party.
From there it will spread. Among everybody at the party. And the tabloid press.
Hiding it will not achieve anything.
Plus, isn't it the reason he was invited? Hiding his headwings is only going to get a response of "huh, Cyra's child's hiding their headwings."
We don't know who's on the guest list. It's entirely possible he'll be a mystery to at least some of the other guests.