Why do people add 디 at the end of names? What does it mean?
It's like (name)디. I don't really know much about context but I see it around from time to time and I just got curious. Is it a thing around Korea?

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it's a slang there is the word '기모찌' in Japanese means 'feel great' 
~띠 is orginated from 기모찌.

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I don't really know but it might actually be double d. But what does that mean?

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Hmm. I don't know what that usage is. It needs more sentence. 
"민수디, 철수디, 하경디" like this? I haven't heard of it.

Oh, does it happen to be "띠?" Such as "민수띠, 철수띠, 하경띠?" 
For example: 앙, 민수띠~!

This?