START /DESKTOP="name with space" ...

"Not strictly illegal" != "a good idea".
Nearly every command and variable function in TCC handles parameters with spaces, most of the time by simply requiring quoting. The name of a desktop seems akin to the name of a file or of a folder.
just seem like normal procedure.

P.S. The restrictions of desktop names are about as lax as they get. From MSDN,
Desktop names are case-insensitive and may not contain backslash characters (\).

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