That's strange that you would be blocked from purchasing a ticket if the names don't match. Do you live in the US? I wonder if it is a type of fraud protection on COPA or their credit processors part.

I can only offer personal experience from when I was in school and didn't have a credit card. If I wanted to book a flight, I would use my parents credit card and reimburse them rather than use my debit card. While my dad and I have the same last name, my mom kept her maiden name so our names do not match. I never encountered problems booking flights on any US based airlines and their codeshares using her card, even if it was an international itinerary.