I always thought the Spanish pronunciation of the name Jesus was pretty well-known, as it's a relatively common name.

... of course, Rowling thought the same thing about "Hermione," and we know how that turned out.

Probably the easiest way to clarify pronunciation would be to have someone address him using the wrong version, maybe he's someplace where he would wear a nametag or show his ID. He could either correct the speaker, or simply have a moment of irritation and mentally be like "Ugh, is it really that hard?"

Rowling clarified the "Hermione" pronunciation a couple different ways in the later books. Once she has a foreign exchange student mispronouncing it and Hermione correcting him, and another time the character addressed by someone who has their mouth full of food, which provides an excuse for a phonetic spelling.

I just looked up the quote.
'Oh, c'mon, 'Er-my-knee,' said Ron, accidentally spraying Harry with bits of Yorkshire pudding. 'Oops – sorry, 'Arry –' He swallowed.