I'm formally an Elizabeth and have always gone by one of the many, many nicknames for Elizabeth. For travel, my travel documents--cruise/airline reservations, etc are under Elizabeth, which matches all of my IDs (DL, passport).
ON the cruise, we very often have the servers ask on the first night if there is another name we would like to go by, and they will write it down and remember. I sometimes don't bother, because it doesn't hurt me for them to call me Elizabeth. On one cruise, though, I had on a shirt themed from "UP" that said "I'm his Ellie" to my husband's "I'm her Carl," so the server called me Ellie the whole cruise. I agreed to it, of course, because it was cute, not far from Elizabeth, and didn't bother me.
I suppose if you hate your given name or are never used to going by it, then by all means, let your servers and room host know you prefer to be called something different.
(Since I also use Elizabeth professionally, I answer to either)