In the article quoted by you "Via dello Zingaro" is repeatedly pulled over to the current name of the street which is, in fact, "Via Cesare De Lollis". In fact it says "via dello Zingaro (today via De Lollis)". In my opinion the persistence of that sign can have two explanations:

• The sign has a historical and cultural value and has been deliberately maintained by the locals and the Comune di Chieti. If, as you say, the change is recent, perhaps the locals who still remember it still refer to that stretch of street as "Via dello Zingaro" even though the street has officially changed its name to "Via Cesare De Lollis" and perhaps it's precisely for this reason that the sign was deliberately kept in its place. In this case, habit prevails over the will to change.

• The Comune di Chieti simply didn't bothered to remove or conceal the old wall sign after officially changing its name to "Via Cesare De Lollis" and it's not the only case of outdated street signs in this town. Note 2217184 (https://www.openstreetmap.org/note/2217184) indicates the presence of a sign with a different name at the beginning of "Via Fratelli Palizzi". The sign says "Via Filippo Palizzi". It can be guessed that "Via Filippo Palizzi", which is the full name of someone, is actually the previous name of that street, and that upon the death of that man's brother the street was consequently renamed in "Via Fratelli Palizzi" where "Fratelli Palizzi" stands for "Palizzi Bros.". In fact in the labels of the street numbers there's written "Via Fratelli Palizzi" and that is the current name of that street.
This is just to say that in Chieti there's a tendency to neglect the signposting aspect. Probably because nobody feels the need to do that. It's only expected that someone have the foresight and the good will to report these irregularities to Comune di Chieti. But until that day we'll rely on OSM unhesitatingly ;)