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
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