Is my website name legal?

[bcnu]

Now you know why people do a "clearance search" before they invest in a company name, domain name or trademark; if someone else in the same field is already using something similar, then they have "priority" over your later use in any related field.

If the SEO NORTH SYDNEY name is already being used as a trademark in any business or marketing channels that COULD overlap yours, you are taking a huge risk of legal troubles.

As you may know, under Australian law (like USA, Canada, UK), there is no obligation to register a trademark; the non-registered rights are enforceable from the moment they first USE the brand on their goods or services.

Bottom line, if you intend to offer SEO services, which are already being offered under the same brand, they can argue that it creates a likelihood of confusion among customers and ask you to stop doing that. If you do not comply, they can (in theory) sue you for an injunction if not also damages (if they have any),

Add: Because you didn't mention what goods or services you're planning to market, nor whether you are marketing anything to anyone in Australia, this is all guesswork.