Maddy is cute prefer spelling
Maddie though. I like Madeline/Madelene/Madeleine/Madailein/Madolyn/Madlen/Madelaine myself. Other ideas:
Madella Madelle
MadgeMagdelene Magdelena Magdelen
Magda Magdala
Maddalina
Madihah mah-DEE-hah Arabic "praiseworthy"
MadonnaMaddox Maddock
Maridel
Maida
MeadeMedeaMadinah Madina
Almadinah
Madora