This is a very strange and interesting sounding name for Erins' isle, does it literally translate into 'ire-land' ? I'm guessing the name is unique because of a somewhat shared ancient history of these two Celtic countries?
To follow on from rmcode's note, the I- in Iwerddon probably comes from an early form of Y (the):
- I + Gwerddon - 'The Green-place'.
The initial g- was dropped following I (as nowadays with Y) because gwerddon is a feminine noun, giving I Werddon. Once the two words were joined through frequent usage the result was Iwerddon.
Iwerddon is the Welsh equivalent of 'Emerald Isle'
Gwerddon from which it is derived is 'an oasis, a glade, a green nook or spot'