No, it shouldn't. That’s what’s sometimes called a "scrivener’s error." The person preparing the document made a minor mistake, but that does not change your father-in-law's intent to name your wife as his agent under the durable power of attorney. It’s not as if he has another daughter named Ann. That's the legal answer. As a practical matter, if your father-in-law is still competent it might make sense to update and correct the durable power of attorney. You never know what some officious bank manager might object to.
For more about powers of attorney, click here.