Still, the main question is about RE Spirit, and RE Fusion's name changing effect disappear when the fusion monster goes to the graveyard, meaning you can't revive this card with RE Spirit even if you used RE Fusion to summon this card.
MBD sometimes counts. It depends on the phrasing used on the card.
An example being a "Red-Eyes" monster meaning anything with "Red-Eyes" in the name and/or in the fusion material. Dual links is more picky than the real rule book. B. Skull Dragon doesn't count while MBD does. Honestly, it doesn't really make any sense... you just have to play test it in Dual Links.