Related to this answer.
Earlier today I was sent a video that showed the Chief Rabbis of Israel at the Kotel making a Mi Sheberach for the refuah of President Trump, where they called him דונלד ג'ון בן פרד (Donald John ben Fred). I was surprised that they used his father's name. The person who sent me the video told me that he thinks he heard that that's the halacha. After digging around here on MY, I found the above mentioned answer (and other answers for that question). The source appears to be the Lubavitcher Rebbe. Are there older sources? What is the reasoning?