Barnhart has been asked by the government to look at ways to update the policy, which has been in place for several decades.
Central Services Minister Nancy Heppner says Barnhart's expertise will help the process.
"There are some concerns about things like ambiguity around language, like if a building is going to have a name pulled off, it talks about being immoral. It's a bit subjective," said Heppner.
Heppner says there's also concern about the committee that looks at naming issues.
It's ad hoc and there are different committee people every time, "so we're concerned about consistency across the board," she added.
Premier Brad Wall also says the province currently can't name buildings for someone who is still alive and he says he's not sure that makes much sense.
Barnhart says names for buildings and landmarks are about recognizing people who helped build Saskatchewan.
Recognizing someone who is still alive is an option that should be looked at, but with caution, he said.
"In some ways, I guess that makes sense, in the sense that it's a way of honouring them and they realize we're honouring them if they're still here," Barnhart said Wednesday.
"On the other hand, you have be careful, I guess too, that those people aren't going to then disgrace themselves later, which would bring embarrassment to the province. So, there are pros and cons, and I'll obviously have to look at that."
Barnhart is expected to provide a report by the end of the year.