This is a Western name so thus has no REAL Japanese equivalent, HOWEVER, if put in katakana, it would most likely be ベッキー(bekki-) Which would be pronounced the same as normal english pronunciation, but holding the ck sound a tiny bit.
When thinking of how to say a western name in Japanese, just remember the sounding of your name and find katakana that sound the same as well. Example: Name Kayla in English is translated to Kaira in Japanese. There is no "L" in the Japanese language and the "Y" is replaced with an "I".
Here is a wiki page that has all the katakana on it:
http://en.wikipedia.org/wiki/Katakana
Rebecca Bardoux's birth name is Rebecca Paulson.
Rebecca Ferdinando's birth name is Rebecca Ferdinando.
Rebecca Epley's birth name is Rebecca Olson.
Rebecca Quagstein's birth name is Rebecca Daskawisz.
Rebecca Night's birth name is Rebecca Hardwick.
Rebecca Miro's birth name is Rebecca Mirone.
Rebecca Withey's birth name is Rebecca Ridgeway.
Rebecca Gullion's birth name is Rebecca Gullion.
Rebecca Hinkle's birth name is Rebecca Sandberg.
Rebecca Holloway's birth name is Rebecca Hernandez.
Rebecca Gallie's birth name is Rebecca Landsberger.
Rebecca Mabey's birth name is Rebecca Clements.