＠Mike I've just checked your Korean level. Okay, you'll see some grammatical terms in this explanation. I'm gonna make it easy, I'm not sure if I can pull off though :b
First of all,「-이」is a descriptive postposition. It's combined with the ending like「-ㅂ니다」,「-에요」,「-죠(an abbreviation for '지요')」
I don't care. 전 신경 안 씁니다.
I'm Korean. 전 한국인이에요.
Who says that way is a moron. 그렇게 말하는 사람이 바보죠.
Second of all, as you saw all of the above,「이에요」is used after a noun ending with the final consonant, and「예요」is used after a noun ending with the vowel.
Let's take「제 동생이예요」to see how the rule works. You know it's wrong. In it,「에」is influenced by the vowel「이」(If you try to pronounce 제 동생이에요, you can find out.) This phenomenon is called "Progressive Assimilation Of Vowels". But the rules of Korean orthgraphy don't reflect it in written Korean, it's why「제 동생이예요」is wrong. Then someone could raise this kind of question, "Isn't reasonable to see this way「제 동생(ending with the final consonant) + 이(the postposition) + 예요」if 제 동생이 했어요 is correct?" Yeah, the matter is that 예요 doesn't exist in Korean as an ending.
About「동건이예요」, the last syllable of「동건」ends with the consonant, so「이」comes to the end of it.「동건」+「이」+「이에요」=동건이이에요. You see two 이s bump into each other in it, and it seem not to follow the economy principle of the language. So it becomes 동건이예요 by shortening「이에요」. As another example, 미희이에요 isn't wrong, just all people abbreviate「이에요」. Keep this in mind, that what comes before「이」is 동건이, not 동건.