Bingo. Or just eircom National League - people will know what we're talking about.
Then the "pyramid" *COUGH* would look like this
National League Premier Division
National League First Division
National League U-20 Championship
National League A Championship
with the sponsor's name on the front, if necessary.
Faddish names like 'I-League' or especially references to Elite are likely to promote ridicule more than anything else.