The various versions of spelling all come from the Ojibwe phrase "misaabe-wajiw," as explained in the Perfect Duluth Day Writer's Guide:

Mesaba Avenue is the proper name for the street that runs along the western edge of Downtown Duluth and the Central Hillside.

Mesabi Iron Range is the proper name for the largest of four major iron ore deposits in Minnesota’s Iron Range. The Mesabi Range is located primarily in Itasca and St. Louis counties; it was known to the local Ojibwe as Misaabe-wajiw, which means “Giant’s Mountain” or “Big-man’s Mountain.”

Mesabi Range College is a two-year college with campuses in Virginia and Eveleth, named after the Mesabi Iron Range. It was originally named Mesabi Range Community and Technical College; the name was shortened in 2014.

Missabe Building is the proper name for the building that stands at 227 W. First St.

Duluth, Missabe and Iron Range Railway Co. (abbreviated DM&IR) is the former name of a railroad organization in northern Minnesota and Wisconsin now known as Wisconsin Central Ltd. It is a subsidiary of Canadian National Railway, which acquired it in 2004 from Great Lakes Transportation. The DM&IR name was dropped at the end of 2011, when CN merged it with the Duluth, Winnipeg and Pacific Railway Co. and the Wisconsin Central. The DM&IR moves Iron Range taconite to Duluth and Two Harbors for shipment to the lower Great Lakes.

Of course, none of this answers the question, "Why in the flippin'-misaabe-wajiw would the five things above have three different spellings?" But it at least lays out some background and a distinction between which spelling goes with which thing.