The Aboriginal peoples and cultures of Australia are as ancient, diverse, and unique as the flora and fauna of its land, billabongs, and sea. A common thread that weaves and connects the different Aboriginal communities are their shared understanding of the 'Dreamtime'; creation stories of how ancestor and supernatural spirits formed the landscape and law of both the land and the cosmos. Dreamtime stories are also represented in ancient hieroglyphs; painted and carved on sacred formations, showing where water, food, shelter, and resources were to be found. These are more than just stories or mythology, as they helped ensure the survival of the world's oldest living civilization. Dreamtime stories are passed on to this day through ceremony, song, and dance; cultural exchange at its purest form. See the video below from the documentary series "First Footprints" to get a deeper understanding of early Aboriginal Australia.
The following image provides a timeline based on what geological and archeological findings have dated as humanity's greatest land and earliest sea migration into the Australian continent and Tasmania.
The end of the last ice age roughly 20,000 years ago brought about an explosion of abundance in resources and with it a massive bloom in cultural and artistic expression. This was occurring in all Aboriginal communities throughout the continent and especially so for those in the northern territories, referred to as Arnhem Land.
This brings us to the different names of perhaps the most iconic symbol of Australia's past and present, the didgeridoo. The origins of the name 'didgeridoo' may stem from a European onomatopoeia taken from the way the instrument sounds. Many didgeridoos are made from readily available bamboo, which may also contribute to the name. The Aboriginal communities in Arnhem Land are especially renown for their masterful playing of the instrument which they refer to as 'yidaki'.
"Many academics and didjeridu enthusiasts find it useful to make a distinction between the yidaki, an instrument made from local materials [such as certain species of eucalyptus] by Yolŋu people from northeast Arnhem Land, and any other didjeridu [made by other Aboriginal communities]."
In any case, the didgeridoo is a common name used by all Aboriginal communities, interchangeable with terms for the instrument in their local languages. See the following article Yirdaki, Yiḏaki, Yidaki, Yiragi. Let’s call the whole thing off for an in-depth listening of the pronunciation. The following chart show several of the over 45 known names.
Image source: https://www.aboriginalart.com.au/didgeridoo/what_is.html