Irish and English.

The generally accepted derivation of Eileen is that it is the Anglicized form of Aileen [or Eibhlin/Aibhilin] which is itself the Irish form of Helen [q.v.].  Chambers suggests Eileen may alternatively be a variant of Evelyn (see below).

A correspondent [ER] notes that her grandmother was baptised Eileen but also known as Helen. By extension she was given the pet name of Nellie.

Another correspondent [MG] has pointed out that scholarly sources now consider that Eileen is Celtic, derived from the Norman French Aveline, and hence equivalent to Evelyn. This may be a case of parallel derivation.