It morphed quickly from Ballaarat to Ballarat as the geographical name. IIRC the railway (opened in 1862) always used Ballarat, and so did maps. The spelling Ballaarat survived as the formal incorporated name of the municipality until the ~1992 Kennett forced mergers: City of Ballaarat, Borough of Sebastopol and bits of adjoining shires were merged as City of Ballarat. The same merger era eliminated the Lillydale vs Lilydale duality, and possibly Queensliffe vs Queenscliff.
IIRC my pre-1992 Ballarat Bitter can, showing Ballarat Bertie, has the geographical version. Here is another related piece of Australian social/technical history:
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www.defence.gov.au/news/navynews/edition...es/eightbells.htm>
Roderick B Smith
Rail News Victoria Editor