My understanding is that the name applies to all Allied troops who held Tobruk in 1941, over half (14,000) included Australian troops, but the rest (some 12,000) being British and Indian armoured / artillery / cavalry.
Over a few months from August 1941, the Australian and Indian troops were withdrawn by sea and replaced by a British / Polish / Czechoslovak force.
Edited to add: It might be one of those labels that has evolved over time, I imagine that the deciding factor is that if a British or Indian soldier who held Tobruk in 1941 deemed himself one of the "Rats of Tobruk", then who's to argue?