What this name more indicates on basis of fact ?
Apart from the name as it indicates ruler of rama, what other information can be obtained looking at the name. If there's any body, you are wel-come to make us understand.
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I am not sure exactly what you are asking, but the etymology of ramesh is that it comes from two roots: ram with cognates in Greek etc., means to please, to rest (and hence, to stop in some usages), to enjoy carnally, to couple, to be pleased, to enjoy oneself, etc. From that one gets ramA, the enchantress, which along with other meanings, is used as a common epithet of the goddess of wealth. The other root Ish, again with cognates like eigen in German, means to be a master of: so ramesha is literally the master of ramA, and is a very common eithet for the central character rAma, the god after whom the epic rAmAYaNa was named.