The authors agree that the surname derives from the personal name Eustachio, coming from the Greek Eustàchios, meaning "the one who gives good fruit". The surname appears in the acts of the Municipality of Milan with the form Martinus Stucchus, and in the lists of fine-wool merchants of the same city in 1393, with the variant Bonulus Stuchus. These records confirm a presence of the surname in the Milan area from at least the 14th century.

R. Brondolo specifies that this is an old surname and describes it as "auspicious", in reference to the favourable character of the meaning of the base name, and places its origin in northern Italy.