Eija-Liisa Ahtila (born 1959 in Hämeenlinna, Finland) is a contemporary visual artist and filmmaker. She lives and works in Helsinki. Ahtila experiments with narrative storytelling in her films and cinematic installations. In her earlier works, she dealt with the topic of unsettling human dramas at the centre of personal relationships, dealing e.g. with teenage sexuality, family relations, mental disintegration and death.
I always thought it was a cognate of the Icelandic name Eyja, which is a noun meaning "island". It was originally a shortening of feminine names that begin or end in "ey" (meaning "isle"), like Þórey, Eyrún etc. But maybe since Finnish is not a Nordic language, it is just a coincidence that they sound the same.
'Eijaa' is only used in old hymns, it comes directly from the Latin word 'eia', but it's not used in real Finnish. 'Heijaa' is also rare on its own and it comes from 'heia' which is an alternative on 'eia'.Aija also originates from this name.
― Anonymous User 12/31/2010
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This is actually a diminutive for Erja or Merja or anything that turns into Eija in a child's mouth.
It would be interesting to know where you got this idea of "eijaa" as an exclamation. As far as I know, it's "heijaa". (Of course there can be regional variation in this but it just doesn't sound like a natural "happy exclamation" since "ei" means "no". On the other hand, "jaa" can mean "yes", so perhaps it's +/-.) Not that I have any other theory for the name's origin, but all the same.