As a monk who grew up sheltered within the Temple with no insight on the outside world prior meeting the other Chosen Ones, Omi would struggle understanding metaphors and slang especially in the English language. (That already established in the show)
When he grows older, he asks his friends on what does the word "Daddy" mean from either a dialogue from a movie or a fanfic he read on the Internet.
This HORRIFIES his 3 friends as well as Dojo.
Eventually, Clay explains the context behind the slang.
Would Omi call Chase "Daddy"?
Chase would forbid it and Omi would feel most uncomfortable addressing his Heylin Dragon such an "ill-fitting and inappropriate" endearment.
Jack might in his wet dream XD
It's definitely the sort of thing Omi would just bring up in conversation, regardless of who was present or what they were doing at the time. Omi's bluntness is a defining aspect of his character, so I doubt he'd take the time to really think through the context he saw the word used in before mentioning it to his friends.
Poor Clay having to explain this to him! He'd probably use some sort of cowboy metaphor or simile that leaves Omi even more confused 😂. Raimundo probably has to chime in to translate for Clay.
I agree that he would definitely ask his friends about it, even if he realised the context was adult in nature - he would go to Raimundo and Clay first, in case it's something that might offend Kimiko (I imagine he grows out of his childhood misogyny, but he probably still worries that there might be certain things he shouldn't ask a girl). Master Fung would just ignore him, and Dojo would stutter out some half-explanation while trying to slither away. Poor Mama Dojo never considered giving Omi the TALK, let alone explaining the various nuances of human mating rituals.
As for Chase... (and naturally I'm assuming this is in the context of Omi being an adult and in a relationship with the Heylin Prince of Darkness)
After learning the correct contextual use of the term, Omi would ABSOLUTELY call Chase 'Daddy'. Once.
And Chase would immediately shut him down. Perhaps even be so mortified he storms out without another word or transports himself away from the situation, leaving a thoroughly confused Omi behind. He doesn't show up again for days, at which point he makes it clear it is NOT something they are going to discuss.
I cannot picture Chase enjoying that particular title, in the bedroom or otherwise. This is a man who sold his soul for eternal youth - I can't imagine being referred to as 'Daddy' in any context is something he'd welcome! Aside from anything else, it's probably an unpleasant reminder of the vast age gap between them - even if Omi is adult and fully able to make his own decisions, Chase will be all too aware of how his tally of centuries casts a heavy shadow over Omi's meagre ration of decades.
And though I doubt it would occur to him at first, after some thought I think Omi would be quite relieved. He's already self-conscious enough about his diminished height; having to refer to his significantly taller partner as 'Daddy' is probably something that would irritate him in the long run!