Where did the name 'Microsoft' come from?

Paul Allen and Bill Gates, then and now.
"Microsoft" is one of those brand names that's so familiar — like Coca-Cola or McDonald's — that you probably don't even think twice about what it means, or its origin. Of the top of your head (no Googles!), do you know where Microsoft got its name?
It's simple really, and even if you don't know right away, it's obvious once you read the explanation. The name is actually a "blend word" of sorts, in which two other words combine to make one.
From a 1995 Forbes magazine interview with Microsoft cofounders Bill Gates and Paul Allen:

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