The Chinese name of the bar is actually 失落月光 which translates into Lost Moonlight.
But the author has specifically included a English name for the bar Lose Moonlit, so yeah I guess thats the name now.

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After my confession ended in failure, I somehow came across a mysterious black notebook that can transform people into beautiful girls. There was only one logical choice—writing down my bros’ names! With this power in hand, I shall become the God of a new world!