Revised Romanization: https://en.wikipedia.org/wiki/Revised_Romanization_of_Korean
Most of the discrepancy in romanization comes from the recency of the current romanization system (Revised Romanization, RR) which became official at the turn of the millenium.
For example, the common last name 김 is romanized as "Kim" under the old MR romanization, while the modern RR transliteration is "Gim". Romanization of names will take much longer to adhere to RR than plain text.
(1) You are mixing up the "-이" subject marker and the "NMc-이" diminutive (an additive to proper name(s) ending in consonant, when referring to the individual(s) in a familiar way).
DLG: 서준이 이야기해 => -이 is a subject marker = Seojun is yapping away.
서준이가 이야기해 => -이, diminutive case (similar to Eng. -ee/-ie/-y which are just endearing additives, ~ "little/young") = Seoyun-ee/ Young Seoyun is yapping away
(2) NMc-아 / NMv-야 are also diminutives. They are used to address the individual(s) directly (vocative case).
서준아, 이야기해! = Oy, Young Seojun, talk! [Direct addressing]