While using regex, character negation can be done but not word negation.
Alternative would be to check value stored in substring like this.
DATA lv_substr TYPE string.
FIND REGEX '^ZBH_[A-Z]{2}_\w+_(.*)'
IN 'ZBH_MM_CHECK_X'
SUBMATCHES lv_substr .
IF sy-subrc EQ 0 AND lv_substr NE 'X'.
"match
ENDIF.