These names were known in an Australian household in the 1970s.

I can add more but they get increasingly obscure - but Flowers was as well known as Turing in the commonwealth in the 1980s.

Early peak Turing was when the Andrew Hodges book ('83 IIRC) got mainstream appeal later that decade, from there the myth grew.

I can't remember the film though, can believe it was more Turing-oriented.

I wonder if Hollywood writers just can't imagine having accomplishments that required work of many great people.

Not just the movie, many books and articles. They often give him credit for what a team of people did (in the war-time code cracking efforts) and barely at all mention the work for which he was uniquely¹ responsible. He deserves huge credit for his life's work, no one of a sensible mind would argue there, but many give him sole credit for the wrong things at the expense of acknowledging those he worked with. From what I know (or I am lead to believe, to be more accurate) of his character I think he would be rather miffed by this.

[1] “standing on the shoulders of past researchers/thinkers” arguments aside, in some places

I'd wager the writers are just pandering to the mores of their audience, who currently seem more inclined to an affinity for cult-like behaviour than sustaining an actual interest in the reality of history.