Is it considered a crime for someone to help a close relative by calling that person's bank on their behalf, with the person himself sitting in the room and willingly assisting, and dealing with the customer care representative of the bank by effectively pretending to be that person (i.e. by saying "I am John Smith" rather than "I am John Smith's son")?
It is in many jurisdictions a crime to misrepresent one's identity, but most if not all such laws specify a "fraudulent intent" or similar language as a required element of the crime.
For example Maryland code § 8-301. Identity fraud says:
(b) Prohibited -- Obtaining personal identifying information without consent. -- A person may not knowingly, willfully, and with fraudulent intent possess, obtain, or help another to possess or obtain any personal identifying information of an individual, without the consent of the individual, in order to use, sell, or transfer the information to get a benefit, credit, good, service, or other thing of value or to access health information or health care.
(c) Prohibited -- Assuming identity of another. -- A person may not knowingly and willfully assume the identity of another, including a fictitious person:
(1) to avoid identification, apprehension, or prosecution for a crime; or (2) with fraudulent intent to: (i) get a benefit, credit, good, service, or other thing of value; (ii) access health information or health care; or (iii) avoid the payment of debt or other legal obligation.
A person is guilty of identity theft in the third degree when he or she knowingly and with intent to defraud assumes the identity of another person by presenting himself or herself as that other person, or by acting as that other person or by using personal identifying information of that other person, and thereby:
1. obtains goods, money, property or services or uses credit in the name of such other person or causes financial loss to such person or to another person or persons; or
2. commits a class A misdemeanor or higher level crime.
I think most other laws on similar offenses will have similar limiting provisions. Obviously if the person being represented knowingly consents to the deception there is no fraudulent intent.
The closest crime I can think of would be the offence of fraud by false representation contrary to section 2 of the Fraud Act 2006.
The specifics of whether the offence has actually been committed would turn on whether the person "intend[ed] to make a gain for [themselves] or another".
Given the example in your post, even if John Smith's son only intended to help his father, it would arguably still be fraud according to the literal interpretation of the statute. Whether it would actually be prosecuted is another matter entirely, I'm not sure the CPS would take it that far or that a jury would be inclined to convict.