When I was a kid, we had an old 78 of this song, and the name was sung "Mile -en - burg" with a long I in the first syllable. I don't know who the singers were.

My mother collected 78's, the older the better. In her 80's, she gave the best of them to a young man who collected old jazz and played it on a radio program. He was thrilled.
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Poppagator, it's no surprise to me that Milne's name has changed pronunciation. In "Milneburg" we have the sounds LNB right in a row in the middle. English may have consonant clusters, but LNB is just too much. So a subtle short e sound was added to make millenburg.

'Milne Street' has this: MLNSTR. (Give us a break!) Milne became Mil-nee.

Have you seen the thread where I talk about my Chinese friend and how she made me aware of English's consonant clusters and how hard many foreigners find them? It's probably not just foreigners that find them hard.