In the US, generally the position is that it's fine unless you're impersonating that person. For example, there was a court case where a Morgan Freeman soundalike did a car commercial or something. The court found that since he was specifically doing a Morgan Freeman impersonation, that was a violation.

Professional impersonators who are doing it for comedy and not misleading people for profit get a pass, like SNL or Frank Caliendo. And Jim Hanks often impersonates his brother Tom when he's not available, but Tom is okay with that because it means he can focus on the important stuff.