The City of Port Phillip website contains information on the history of Port Phillip. The following is an extract about the history of Port Melbourne

Port Melbourne was first called Sandridge after the ridge of sand dunes along the beach. In 1839 Wilbraham Frederick Evelyn Liardet arrived with his wife and family and set up home at the beachfront. Liardet has been called the father of Port Melbourne for his many innovative and entrepreneurial ventures which included building the first rudimentary jetty and providing a mail service to Melbourne from the port.

In 1850 the first land at Sandridge was sold, although the area had been surveyed as early as 1839. The most distinguishing feature of Sandridge at the time was the great saltwater lagoon as large as the settlement itself. The importance of Sandridge as the port for the metropolis was underlined when the first passenger railway in Australia was opened on September 12, 1854. It ran from Melbourne to Sandridge.

On 13 July 1860, after some agitation for self-government, Sandridge was proclaimed a municipal district. William Morley, a local coal merchant, became the first chair of the Council. Sandridge became a borough in 1863, and in 1884 changed its name to Port Melbourne. In 1893 Port Melbourne became a town and, on 14 May 1919, was proclaimed a city.

In June 1994 the City of Port Phillip was formed from the old municipalities of South Melbourne, St Kilda and Port Melbourne.

The first Council offices opened in 1861, located on the corner of Bay and Graham Streets, Port Melbourne. The first community hall was built in 1869 on the current site of the Port Melbourne Town Hall. In 1881 the addition of the grand building in front of the hall brought the council chambers and offices to the site.

Source: https://www.portphillip.vic.gov.au/explore-the-city/history-and-heritage/port-phillip-history