The supplier should make good. Some require a buyer to cover the cost of shipping replacements and some do not. So give the seller a chance to make things right. It they do not, then by all means post the name. I would also say that if they do make good, also post the name.
One reason for posting is to help others avoid the seller and the other is for others to know that they are reputable and so might buy from them in the future.
I am one who offers a buyer the right to choose a refund or a replacement. I am willing to pay half the shipping for replacements unless the entire lot arrived dead. Then I may not have enough fish to replace the order and so I will refund the entire cost including the shipping.
The worst 18 moinths I had shipping/selling fish was when I had a batch of bad bags that were killing fish. I changed suppliers and have never had that problem again. That episode cost me about $4,000 reatil value, in DOA fish ove that year and a half.