Yes, you can run into problems for copyright infringement if you copy someone else’s original design (copy included), but, as pointed out, it could be a pre-made template as well. It’s important to know this to see if you could get in trouble for taking your site live.
As far as the seller’s work, it all comes down to what was agreed upon and how much you’ve paid.
As a rule of thumb if you paid anything less than $80 you probably got stucked with a generic design, from a, most likely, nulled (cracked) theme.
A seller receives $64 from a $80 order, and WordPress premium themes starting price point are $50-$60, so from this it might be easy to figure out which is which.
Are they using a premium theme? Ask for its license! If they cannot provide then ask for a refund…regardless of how much you’ve paid for it.
If that’s not the case and you’ve paid less than $80 I wouldn’t ask for a redo as you got your money worth of labor, but if you paid more than that then I would read their gig carefully to see who dropped the ball and act on it id it’s your right.
And it’s important to notice that website creation is different than a custom design.