You can register a company without choosing a name at all — the registration number becomes the name until you change it. That is a legitimate option and more common than people think, particularly where the trading name is going to be different anyway.
If you do want a name, it is worth understanding what registering it does and does not give you.
Reserving a name
You apply, submit alternatives in order of preference, and the CIPC checks them against existing names and against the rules on what a name may contain. Names that are confusingly similar to something registered, or that suggest a connection you do not have, get refused.
Submitting several genuinely different alternatives rather than four variations of one is the practical tip. Four versions of the same rejected idea all fail together.
A company name is not a trade mark
This is the important one and it surprises people regularly.
Registering a company name stops nobody else from registering a similar company name in a different form, from trading under it, or from using it as a brand. It gives you an entity, not a monopoly on the words.
If the name carries real commercial weight — you are building a brand, you will advertise under it, customers will search for it — that is a trade mark question and it is a separate process worth taking advice on. The time to do it is before you print anything, not after somebody else has.
Check the name is actually available in practice
Before committing, search for it as a customer would: the domain, social handles, and whether an existing business is already using it in your line of work.
A name that clears at the CIPC and is already in use by a competitor two suburbs away is a name that will cost you money in confusion, and possibly in a dispute.
Trading names
You may trade under a name that differs from your registered name, and plenty of businesses do — one entity operating several brands, or a registered name nobody uses commercially.
What must appear on invoices, contracts and official documents is the registered name and the registration number. The trading name can sit alongside it; it cannot replace it.
Choosing something that works
Practical rather than clever: sayable over the telephone, spellable after hearing it once, and not so narrow that it limits what the business becomes. Names that describe a single product or a single suburb become awkward the moment you add a second.
And check what it means in the other languages spoken by your customers. That is a two-minute conversation which occasionally saves an expensive one.
General guidance, not legal advice. Trade mark protection is a separate matter; take proper advice where a name has commercial value.