Property I'm buying says under offer when they've accepted my offer. Is this right?

[Neaoll]

Surely it should be said sold stc?

I'm about to pay out for a survey and it's still showing as available on Rightmove

That's usual on Rightmove. Although annoying when you are the buyer. Different estate agents seem to do it different ways and by placing it Under Offer it lets others know that it could still fall through (hoping not for you). It changes to Sold when you exchange contracts but not always. We moved 6 years ago and the house we bought is still showing as under offer if you look at the house price listing!
Congratulations on your new home.

Ours says sstc on rightmove and we haven’t exchanged yet...

Under offer and SSTC mean the same, in fact under offer makes more sense.

That’s right, it’s under offer- your offer. It hasn’t sold yet.

Ah that's strange mine is listed as SSTC when we haven't exchanged

Doesn't it just encourage someone to gazump?

When you make your offer you can specify that it is subject to it being listed as such at the estate agents

To be honest anyone can gazump anyone until contracts are actually exchanged. I used to work in conveyancing and we had people who made offers on a property just by knocking on the door and asking if they’d consider xxxx offer right before they were due to exchange!

Perfectly normal to show as either under offer or sstc - they mean the same thing.

You can make your offer conditional on it coming off rightmove etc. Then it won't show up as anything.

Yes. Some EAs use 'under offer' until exchange then change status to 'sold stc'. Some list at 'sold stc' as soon as an offer is accepted. 'Sold stc' standards for either 'sold subject to contract (exchange)' or 'sold subject to completion'. I really wouldnt be concerned