SO, SO I WAS THINKING OF FAKE SCENARIOS AS YOU DO...HERES A LIST OF NICKNAMES I FEEL LIKE THE ETERNALS WOULD USE:
Ajak: She'd probably call you by your name, or like 'Child' or something. Because she's like a mother to everyone.
Sersi: She'd just call you 'love' because it seems like it would suit her voice and tone.
Ikaris: He'd either EXCLUSIVELY refer to you as your name, or he'd give you dumb names like Pipsqueak, etc.
Sprite: Sprite would be creative and come up with fun ways to refer to you depending in you dynamic with her. Like, she'd use 'Bro' as a gender neutral term, and 'asshole' is her go-to nickname.
Kingo: Oh, he'd love creating extended metaphors and just fun names out of say what your powers are. (e.g 'you oversized lightning rod' for Ruby when she's fully made of metal.)
Thena: Out of respect, She'd refer to you as your name. But if you get closer She'd use a shortened version like Gil for Gilgamesh. if your name can't be shortened, she'll ask what you prefer as a nickname.
Gilgamesh: He's definitely the kind of guy to come up with a nickname, realise it's an insult and then apologise. Tell me I'm wrong.
Druig: If he likes you, he'd call you teasing nicknames because I'd like to think he's quite mischievous and the kind of person to use insult humour. If he doesn't like you that much, he'd just stick with your name. Simple, really. But in a relationship, he'd use some really butterfly-inducing adjectives. 'beautiful' 'gorgeous' 'darling' 'sweetheart' and he would always use a specific tone as well.
Phastos: He's so nice to his actual friends and so respective of boundaries that I think he would ask you what you prefer to be referred to as, before going into a small rant about identity.
Makkari: Now, this is where I keep drawing blanks. But I think a nice simple 'Angel' or 'Dear' would be nice if you were together. As friends, it'd just be your name.