If you want to convert to a Unicode encoding without the byte order mark (BOM), add the endianness to the encoding, e.g. instead of "UTF-16" which will add a BOM to the start of the string, use "UTF-16BE" which will convert the string without adding a BOM.
i.e.
<?php
iconv('CP1252', 'UTF-16', $text); // with BOM
iconv('CP1252', 'UTF-16BE', $text); // without BOM