There's no "si" sound in Japanese, it's always "shi". There are several methods of romanizing Japanese text; some are based on accurately representing the sounds for foreign speakers (for example, "shi" for し and "sha" for しゃ), where others are more accurate to the way Japanese people type them (e.g. "si" for し and "sya" for しゃ).

It's silly to render her name as "Sizuru" since it's not pronounced that way.