There is no legal barrier to adults choosing to have the same surname, regardless of whether they are in any type of relationship. Doing so has no legal effect on the status of the relationship but it may remove a lot of practical difficulties, particularly for de facto couples (in such matters as hospital benefits, making contracts, obtaining a loan), simply because there is likely to be less explaining to do.
You can change your surname by applying to Births, Deaths and Marriages Victoria (contact details). Information and forms may also be obtained and lodged via the Births, Deaths and Marriages website at www.bdm.vic.gov.au. (For further information, see Changing your name.)
The surname of children of a de facto relationship is also discussed in Changing your name. Note, however, that one parent cannot change the legal first name or surname of a child without the other parent’s consent or a court order. See “Registering children conceived with reproductive assistance and through surrogacy arrangements”, for information on registration of children born to same-sex parents.