King al-Ḥasan of Morocco (officially romanized as Hassan, with a double ss, due to the influence of French orthography) is an example of the former.
The early Islamic poet Ḥassān ibn Thābit is an example of the latter.
In the original Arabic, the two different names are easily distinguished.
Hassan or Hasan is an Arabic given name and through the influence of Arabic, languages spoken by Muslims such as Persian, Kazakh, Kurdish, Urdu, Indonesian, Malay, Turkish, Uyghur, Turkmen, Somali, Swahili, Berber, Azerbaijani, Crimean Tatar, Tatar, Bosnian, Albanian, Bengali, etc.
Therefore, depending on language and region, spelling variations include Hasan, Hassen, Hasson, Hassin, Hassine, Hacen, Hasen, Hesen, Hasin, Hassa, Hess, Cassin, Chazan, Chasson, Chason, Khassan, Khasan, Chessar, Casan, Casen, Hasso, Lassana, Alassane, Lacen, Lasanah, Assan, Asan, or Haasan (Haasaan, Hasaan, Hassaan).