It was pretty difficult to conceal that Azriaphale was an angel and he was a demon given that the magic of these worlds made it impossible to hide his wings. They sort of stood out in a crowd. So, he hadn't seen any reason to be cagey about it especially since...

"He'll try to join you!"

Spoken with the horror still in his voice.

"It would be you and him and those stupid little demeaning tricks... Ugh, the wiggly wand bit in which you just wave a stick around like it's actually doing anything or making the ball disappear by shoving it up your sleeve... And children's parties! Cake everywhere... Just do us both a favor and don't mention it!"