Can I change the owner of a 3 iPhone contract if I ring them (I'm over 18)?

I pay monthly for my phone with my card but the account is in my moms name and I want it in my name.

She set up the contract but if I ring 3 can I put it in my name? I'm the owner of the card that pays and I'm over 18.

Is it possible to transfer?

It should be possible. Though you may need some proof of authorization from your mom. A letter, or if she would be available to validate that through the call.

Not usually. The original contract is in your mum's name and was entered into after she passed a credit check. Switching the account into your name means that 3 have to go through all the same fixed costs as they do when taking on any brand new customer and you'd also have to pass a credit check. They'd also have the costs of checking with your mum that she's agreed to the change.

All that means that 3 are highly likely to simply refuse the request and if they do they'll charge a significant administration charge to reflect their costs of making the change; it may be higher than their actual costs simply to put you (and anyone else) off the idea as it's absolutely not in their interests to do it, and would add a large administrative workload if it became a commonplace service to their existing customers.

All of the above is informed speculation based upon experience. If you want an answer you can rely on then ask 3 directly as theirs is the only answer which matters. As you're not the present account holder they will not speak to you at all about your mother's account, so it's best if she makes the initial enquiry.

She will have to cancel the current contract, then you can replace it with one of your own.

All that means that 3 are highly likely to simply refuse the request and if they do they'll charge a significant administration charge to reflect their costs of making the change; it may be higher than their actual costs simply to put you (and anyone else) off the idea as it's absolutely not in their interests to do it.
Not usually. The original contract is in your mum's name and was entered into after she passed a credit check. Switching the account into your name means that 3 have to go through all the same fixed costs as they do when taking on any brand new customer and you'd also have to pass a credit check. They'd also have the costs of checking with your mum that she's agreed to the change.

Contracts are non-transferable. So your mother needs to cancel the contract and then you can open a new contract.