Pretty much what the above posters said about books making up name meanings. I have found that when a name book writer can't find (or can't be bothered to find) a name's meaning, they put either "brave" or "beautiful" as the meaning!
However, it's possible that
Kelsey, originally a place name, comes from ey ("island; peninsula") + the Old English name Cenel meaning (from "cene" meaning "brave; fierce; valiant"). It may also come from Ceolsige, from Ceol meaning "ship; small flat bottomed boat" + "victory." Ceol was also used as a name in Old English.
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http://www.namenerds.com
http://www.behindthename.com/pnl/67246