There is nothing ambiguous about it, because it's the same pronunciation. It's a convention of how this particular name is spelled.

But does German have ambiguities here? Yes, it does. In the instrument 'Oboe', the 'oe' is pronounced as two syllables: long 'o' plus schwa. It cannot be written with 'ö'. It should better be written 'Obohe' (my controversial proposal). And dialectally/regionally, 'oe' may be long 'o' instead of the 'ö' sound, like in the city of 'Soest', which could be written 'Sohst', but then people from that city would complain (about tradition, maybe).