I assume you are looking for Doman Street (or around there). A breakdown of the search results can be viewed here. The listed address information is used for displaying the results you got.
I figure Pregan Island is the closes hamlet node of it’s kind to Doman Street which is why Nominatim, the search engine for OSM, is using that. I have no knowledge of Wagga Wagga or Pregan Island but superficially it seems that place=hamlet is not quite fitting for Pregan Island as it seems to be no more than an empty field. It also seems like a rather old data import.
My first thought would be to downgrade the node to place=locality, depending on the significance of Pregan Island. Which hopefully you might know more about.
Thank you very much Kartonage your assistance was excellent.
While I fully agree with you that place=locality was more fitting than place=hamlet, I went to the New South Wales Geographical Names Board, who state it is a “rural place” and also says “A locality at Wagga Wagga comprising the partially enclosed area between the Murrumbidgee River and the Parkan Pregan Lagoon, 1 km S of the suburb of North Wagga Wagga.”
I also only know Pregan Island as being an area included in the suburb of North Wagga Wagga.
I have downgraded the node to place=locality and trust that this will amend the inaccuracy of Pregan Island being included in the coordinate search previously mentioned.
Thank you so very much, I am most appreciative of your help.