You'll want to refer to your warranty documents. The terms and coverages will be stated in gory detail there.
But generally parts replace under warranty will be covered under the original unit's warranty. So if you had a 2 year warranty and the blower motor was replaced after 1 year. The new motor as well as the rest of the covered parts would be covered for another year.
But again, the details are in your warranty papers. Nothing said here will make any difference to that.
The OP later added:
The warranty for the original installation has already expired, so I
had to pay full price for the blower.
In that case it's entirely a transaction between you and the servicing company. If they offer no warranty on their parts or labor then my recommendation is that you choose another company that does. In my experience there is usually some language printed on the invoice that details any warranty for services and installed parts. In my experience that is often 30 days or so.