My guess would be from the Sanskrit ramesa, Rama (name of Lakshmi) and isa 'ruler' so 'ruler of Lakshmi'. Ramesa was a name of Vishnu and occurs from the Puranic texts on and was born by authors and characters from medieval times.
If that is the source, I probably wouldn't use it for a baby girl, even if you're not practicing Hindu. It may well be from an entirely different source that I don't know of though so based only on the sound it's very pretty for a girl.
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