Some CPAs are up in arms about a move by their industry’s main trade group to allow people from outside their ranks to be credentialed to help companies value complex assets.

Caught in the crossfire: companies that more than ever need specialists to help assess hard-to-value assets, like brand names and customer relationships. The demand for such services has grown dramatically in recent years into an industry that generates more than $4 billion in annual revenue, as those assets have grown more prominent on companies’ balance...