I can think of one thing which could've potentially contributed to the change in spelling between TOS and TNG: the British TV series Star Fleet. Star Fleet (1982) was the English-dubbed version of a Japanese puppet-animated series in the mode of Gerry Anderson's "Supermarionation" series.
X-Bomber was renamed Star Fleet and dubbed by English speaking actors
for broadcast in the UK on ITV. The show was broadcast there on
Saturday mornings, first airing on October 23, 1982, the day before
Star Wars' UK TV Premiere.
The logo used in the English-language "Star Fleet" version of the TV series clearly spaced the title out as two words:
–Star Fleet Wikia
This doesn't seem to be a trademark issue, though. I can't find anything in the UK Intellectual Property Office's online trademark search, which claims to hold UK trademark records from 1876 through the present, indicating that "Star Fleet" was trademarked in association with the show.
However, "Star Fleet" was fairly popular - most notably, the year after its release in the UK, Brian May (of the rock group Queen) gathered a group of musicians to record an EP based around a cover of the show's English theme song.
This is by no means definitive - the lack of any record of a trademark conflict dispels the most likely connection - but the brief success of a TV series using the two-word term may have inclined future Star Trek staff and fans to differentiate their Starfleet with the one-word term.