Would it also be 'hadhihi' instead of 'hadha' when describing a female neighbour?
Arabic names are difficult to transliterate in English; I've seen my own name written in at least 5 different ways. Thus, I would advice caution in general (not only on Duolingo). However, using ou here is not appropriate, because it's a short vowel. You can write Mohammed though, that's a common spelling.