The term "3.5" was definitely in use by fans even before WotC made any announcement about a new edition. For example, this
ENWorld post (titled "3.5 D&D?") from March 2002 speculated that the upcoming new version of the Stars Wars RPG was an indication that WotC might also revise the 3e rules.
WotC made the official announcement of the new edition on 5th December 2002 (archived copy
here), but that announcement did
not refer to it as "3.5", only as a "revised edition". This
post from 27th December 2002 is the earliest reference to "3.5" I could find on ENWord after the announcement and that seems to predate any public WotC use of the term.
According to
this page, WotC staff referred to the new edition as "3.5" during an (invite only) RPGA event at the Winter Fantasy convention, which took place at the end of January 2003, so they were definitely thinking of it as 3.5 by then.
The earliest official reference to the new edition as "3.5" in
Dragon seems to be in the article "Revision 3.5 Update" in February 2003, where Ed Stark wrote "Think of it as a “3.5” edition of the game, much like a software upgrade." The use of quotation marks at this point is interesting. By the end of February, there was a
3.5 logo, so WotC was fully committed to that nomenclature by then.
It is entirely possible that the revision was thought of as "3.5" internally by WotC from the beginning. However, since the initial announcement didn't use "3.5", and fans were apparently using that term before WotC officially did, it is at least a possibility that the D&D team followed fans' lead on the matter.