Why the bay is in the name
Bröd means bread, and the bay is Hobsons Bay. The suburb they meet in has been receiving people off ships for most of its history.
Bröd means bread. That is all it means, and it is pronounced closer to brurd than to brode.
The ö is not decoration and it does not come off. A word spelled brod in Swedish is a different word, and dropping the diacritic to make a name easier for an English keyboard is the sort of small surrender that ends with a bakery calling itself Scandinavian-inspired. The website address is ASCII because addresses have to be. Everything else keeps the ö.
Which bay
Port Melbourne sits about four kilometres south-west of central Melbourne, with the Yarra along its northern and western edges and water to the south.
That water is Hobsons Bay, which is the northern arm of Port Phillip. So "by the bay" is accurate at two scales, and the one you can see from the foreshore is Hobsons Bay.
Before any of it was built, the site was dominated by a large saltwater lagoon.
Sandridge
It was called Sandridge first, and before that it was known as Liardet's Beach, after Wilbraham Liardet, who arrived in 1839 and put up a hotel and a jetty and ran the mail.
Australia's first railway line opened here in 1854, running from Melbourne down to Hobsons Bay to serve the pier. The pier opened the same year as Railway Pier and was later renamed Station Pier. The borough separated from Melbourne in 1860 and the name changed to Port Melbourne in 1884.
Also 1854, and pleasing to me: the Swallow and Ariell steam biscuit factory started production here. There has been somebody baking commercially in this suburb for a hundred and seventy years, which is longer than most Australian food traditions have existed.
The pier
Station Pier was the main way people arrived in Victoria after the Second World War. It is on the state heritage register, cited for what it shows about how passengers and cargo were handled from the twenties through to the seventies, and it still takes the interstate ferry and the cruise ships.
I am not going to make more of that than it deserves. But a suburb whose central structure is a pier that a large part of post-war Victoria walked off is a reasonable place to bake somebody else's national baking tradition, and it makes the arrangement feel less like an import and more like the ordinary thing this stretch of coast has always done.
The resemblance, honestly
Sweden has a great deal of coast and a habit of building towns that look at water. Port Melbourne looks at water. Beyond that I would not push the comparison — the light is different, the temperature is very different, and a red timber house on a Swedish shoreline is not a warehouse conversion on Beach Street.
What the two places share is the specific ordinariness of living beside a working bay: flat morning light, wind that arrives from the water, and a foreshore that people walk along in every weather because it is there.
That is enough to hang a name on. Bread, and where it is made.