Originally, the common name for mechanical writing machines was “typograph,” a loanword from the print industry, which likely would have caused confusion except that early typewriters were generally unsuccessful. The Purkis “Duplex Typograph” was the first to be named a typograph, and “typograph” dominated until the introduction of the Sholes & Glidden “Type Writer” in 1874.
Gradually, people dispensed with the space or hyphen in “type writer/type-writer,” settling on typewriter (see 1890 commentary here). But even, then, not everyone was satisfied! See here:
The Shorthand Review (New York), September 1892 –

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Ooh, I like “Typine” (:
At least the last two terms survived.
“Typine” sounds zoological.