There is a Bengali name মৌসুমি pronounced moushumi. The origin is ultimately Arabic مَوْسِم, he who marks (or brands) or somthing like that, meaning season. mausam in various pronounications is the common word for season in Persian, Urdu, and Hindi, and mausumi is a pretty common adjective in Bengali meaning seasonal. It is especialy used in the word for the monsoon (which goes back to the same Arabic word through Portuguese monção and influenced by Dutch monsun) winds.
There is no one correct spelling of the name in Roman script, I give it Bengali script above. The Harvard-Kyoto transcription would be mausumi (consonant m with vowel au, s with u, m with i). Many Bengalis would write Mousumi or Moushumi or varieties of that to get the Bengali pronounication across.