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One thing to say is that generally ash-trees in Italy il less common than we think. The "ornello" in Italian is a sort of ash, but it is not really an ash-tree.
In spanish the ash-trees are called "fresnos" there not any word "ornello" in Spain.
In Italy surnames derived from "frassino" are always local or regional they do not exist in Southern Italy:
See surnames like:

FRASSINI
FRASSINETI
FRASSINELLI
FRASNELLI

See spanish surnames from "fresno"

Fresno
Freseneda
All catalan variants: Freixe, Freixa, Frexa, Fraixeda,etc
Galician variants: Frege, Freijo, Fregenal, etc

Possibly there two italian variants , from "ornus":
Orno
Ornato.