Is it correct to say "I prefer to get refunded on my original account" while a store asks me what refund option I would choose?
To answer your actual question, prefer 'to be refunded' rather than 'get refunded'.
The result will be that you 'got a refund', but 'get' with the verb 'refunded' sounds odd to me.
Some other points:
'I would prefer' - if you just say 'I prefer' it sounds habitual, a general preference for all refunds in your life;
'to the original account' is better than 'on my' I think, but then you need to say something like 'I would prefer the refund be to...' too;
'when a store', not 'while', as DS said;
'a store' doesn't really 'ask' you anything, the employee does, but it's OK colloquially I suppose, particularly assuming in your real sentence it would be a specific company name ('Amazon asked me ...' sounds much more natural than 'a store asked me' to me, not that it's actually any more correct);
'which refund option' - that's routinely messed up by some native speakers, so don't worry much, but in general think 'which from a list' & 'what free-form text';
'I would like', or 'asks me to choose a refund option' - 'which I would choose' as you wrote sounds like it was a hypothetical: 'if we were to refund you which would you want'.
That would not be a usual way of expressing that idea, and might confuse a fluent speaker, it would surely sound odd to many native speakers.
We do not usually speak of a person "getting refunded" but rather of a person "getting a refund".
We do not usually say "on my account" to indicate where a refund will go, but rather "into my account", or often there is an indication of which of several possible accounts will be credited.
Thus instead of:
one might say
- I prefer to have the refund go to the account I used to make the purchase.
- Please send the refund to the account I used to make the purchase.
- I would like the refund put on to my Visa card ending in 1827
- Please credit this card [showing the other person the card] with the refund
- Please credit my account with the store.
- I want you to apply the refund to the same account I used to buy it.
- I want to get the refund in cash.
Another answer suggest (indirectly):
I do not think this is natural or indeed correct. A person is not refunded, money is refunded. A person gets or receives a refund.
By the way, the form
is incorrect. You very likely mean "when a store..." as "while" would suggest that you talked over the clerk's question.