The orthography in euskera is Elortegi, without "u", and the spanish Elortegui has the same sound.
In a modern way, the pronunciation is Elótegui, with stress at the ó letter.
The actual euskera speakers around Maruri make this pronunciation.
At Madrid and other spanish speaking zones, the stress use to be changed to the e letter, much easier for
those people with difficulties with the basque names.
Curiously, we have not found anywhere the supposed original form, Elorregui.
In our search, we have found old documents with our name written as Erortegui (most of them at Maruri, Munguia,
Gatica and some times at Lauquiniz), Erostegui (at Gorliz and Guipuzcoa), Elorttegui (always at Arrazola y Durango),
Herortegui, Crorregui, Serategui, etc.
Even we have found documents about Matia de Echeurtegui Saez (b. 1616), a name that does NOT exist in euskera.
Our investigation gives as result he was a brother of Martin de Erortegui Saez (b. 1611), Mara de Herostegui Saez, (b. 1612),
another María de Erortegui Saez (b. 1619), and Domingo de Erortegui Saez (b. 1623), all of the were the sons and daughters of an Erortegui
previously identified. The name of the mother, Maria de Saez, and the second name (in the spanish tradition, the name of the mother is conserved as second
name), Saez, is the same for all of them and the place of birth is Munguia.
Evidently , the orthography of the name is not simple.