[masaegu]

Of course it makes a difference. You have to choose from the five 'r-related' katakana (ラ・リ・ル・レ・ロ) that exist.

Rachel =　レイチェル

Let me add that it's not so much a matter of how a name is spelt in its original language as how it's pronounced. The Japanese take a look at the pronounciation and say it within their own sound system. This is the same process for any language when it takes in a new word from another language.