Until now, that is.
E! News can exclusively reveal that their kids are named Poppy and Charlie.
Moyer referred to them by their names Tuesday night at the season six premiere screening of True Blood in Hollywood.
After mentioning that his 10-year-old daughter from a previous relationship, Lilac, was leaving for sleep-away camp this weekend, Moyer said he and Paquin planned on spending Father's Day "hanging out with Charlie and Poppy."
Paquin said she does have a Father's Day "surprise" for Moyer, but wouldn't spill on details. "I can't tell you because that would ruin the surprise," she laughed before adding, "I don't know about [it being a] big surprise, but yes, there are plans."
Big or small, we're sure Moyer will love every bit of it.
FYI: The new season of True Blood premieres on HBO on June 16.
For more scoop from the True Blood premiere, tune into E! News tomorrow at 7 p.m. & 11:30 p.m.