The band changed its name to Rise Against in 2001 and made its first album , The Unraveling ( made by veteran punk maker Mass Giorgini ) on Fat Wreck Chords that same year . The band changed its name to `` Rise Against '' in 2001 and released its first album , The Unraveling ( produced by veteran punk producer Mass Giorgini ) on Fat Wreck Chords that same year .