The prevailing trend has been not to call George W. Bush “Jr.” because the rules of naming someone “junior” mean that all of his names are the same and “Sr.” was “Herbert Walker.” Theoretically, the same rule applies to the use or II, III, etc.
But regnal names use these suffixes and we tend to refer to presidents by their last name alone, less frequently by their first name and rarely by their middle name. Even if they weren’t related, Bush II still works for me. This means Adams II, Harrison II and Roosevelt II should work as well. Fine. In each of those cases there was a relation.
Yes, sure, there’s a distinct tone of accusation in the use of II or Jr. for Bush that he is somehow aristocratic.
If the fucking gold-plated shoe fits…