You're trying to stump me!

Actually, all four seasons have dual names. I'll fill in the blanks:

1. Fall / Autumn

2. Winter / Cold (not typically used as a season name, but...), also known as Yule or simply "Winter" is paired with "Cold" is not typical, though

3. Spring / Vernal Equinox or simply Spring

4. Summer / Estival or Solstice (not commonly used in English-speaking countries), also known as Warmth or simply "Summer"

But if you're looking for more "common" dual names:

1. Fall / Autumn

2. Winter / Chill

3. Spring / Vernal Equinox (or just Spring)

4. Summer / Estival Solstice (or just Summer)