Hmm...I think you're right, and it would be spelled ジョナタロー. Have you heard otherwise? Oh, and by the way, the particle "wa" is spelled with the hiragana character は but pronounced as wa. Example: ジョナタローのでんわばんごはなんばんですか。 Jonatarou no denwa bango wa nan ban desu ka? What is your phone number? As you can see in this example, わ is used for a "wa" sound inside a word. でんわ means telephone and is pronounced as "denwa", but the particle wa always uses the は hiragana character which is otherwise pronounced as "ha".

In my opinion, you can choose whichever you like, ジョナタロウ or ジョナタロー because it's like a nickname, TAROU is originally from Japanese and there's no specific rule in this case. However, for example, for New York, we shouldn't write ニュウヨウク because it's the English word(s) and we usually use "ー" for the long vowels. (It is used for "cake", too, because it's from the English word.)