Cancelling your ABN or deregistering your company doesn't automatically cancel everything attached to the business — a few registrations need to be dealt with separately, or they keep renewing (and costing you) indefinitely.
Business name
A registered business name doesn't lapse automatically when an ABN is cancelled or a company is deregistered — it needs to be cancelled separately with ASIC. Left active, it will simply come up for renewal (generally one or three years) with a fee attached, for a business that no longer exists.
Trademarks
If the business held a registered trademark, it doesn't cancel itself either. You can voluntarily remove a trademark from the register, but there's no urgency the way there is with a business name — a registered trademark isn't accruing fees the same way, and depending on the situation, it may be worth transferring it (if it has ongoing value) rather than simply cancelling it. This is worth a specific conversation with an IP lawyer if the brand has any residual value.
Domain names and hosting
Domains renew automatically by default with most registrars — cancel the auto-renewal or let it lapse deliberately, but be aware that simply doing nothing means continuing to pay for a domain attached to a closed business, sometimes for years. If the domain has resale value, consider that before just letting it expire.
Software and subscriptions
Beyond the business name and domain specifically, this is a good checkpoint to do a full audit of anything on autopay — accounting software, invoicing tools, industry-specific subscriptions — and cancel deliberately rather than discovering charges on a card statement months later.
The order that avoids problems
Deal with the business name and any trademark cancellation around the same time as the ASIC deregistration or ABN cancellation, and handle domains and subscriptions as a separate admin sweep — they're not eligibility-blocking, but they're exactly the kind of loose end that costs money if ignored.
This is general information, not legal advice — talk to an IP lawyer if a trademark or domain has real ongoing value before deciding to cancel it.