* -라고 불러달라 => This is a literary sounding phrase. -라 is a dramatized way of saying something, usually not addressed to a particular person. For example, 조국이여 영원하라 (May the motherland last forever), 배고픈 자들이여 내게로 오라 (Starved ones, come to me). (There is a smilar -아/어라, as in 와라, which is informal, but 불러달라 is not that) * -라고 불러주세요 => This is a natural sounding phrase often used in real life. We'd say it like this outside of a close circle of friedns (where we'd say 불러 줘). * Another tricky thing is the verb 달다 in 불러달다. -아/어 달다(to want someone to do something for oneself) is a funny verb in that it never seems to come at the end of a sentence in original form. It usually appears in the middle in a connective form, as in 달라는, 달라고, 달라면서, 달라고 해도/달래도, etc. When we mean it as the main verb of a sentence, we usually switch to 주다, because we'd rather say "You do something for me / You give it to me" rather than "I want you to do something / I want it from you". So it rarely appears at the end, except in some old forms now rarely found (이것 좀 해 다오), or literary phrases like your 불러 달라. In short, 주다 is used as the main verb when you're asking someone to do something or when you state a completed action. 달다 mostly appears in the middle of a sentence to show someone's intention of wanting something.

라고 불러달라 for close people(also same ages or younger). 라고 불러주세요 for older people or people you dont know(strangers)

라고 불러달라 for close people(also same ages or younger). 라고 불러주세요 for older people or people you dont know(strangers)