The "Italian sounding" issue
Answer
An Italian-sounding product is one whose name suggests it was made in Italy. The words in the name when read, sound like Italian words or names to an English speaker even if they aren't genuine Italian words or names.
Nuance
For a native English speaker, there is no judgement implicit in the phrase. The expression "X-sounding" where X is the name of a language is just normal English, e.g.
"What is the name of your new girlfriend?"
"Valentina."
"That's a very Spanish-sounding name. Is she Spanish?"
"Yes, she's from Madrid."
The term is completely neutral.
Generalising
We don't have to specify the nationality, e.g.
Did she leave a name?, asked Pereira. It was a foreign-sounding name, replied Celeste, but it's slipped my mind. Pereira Declares: A Testimony By Antonio Tabucchi.We don't have to talk about a nationality. Here are some examples with 'name', Google ngram: a * sounding name
In the expression, "X-sounding Y" the X does not have to be a language and the Y doesn't have to be a name. We could talk about 'a raucous-sounding orchestra'.
Usage in marketing
In terms of marketing, this refers to a very common phenomenon. For example, in the UK we see many power tools that have 'German-sounding' names. This is because (leaving to one side the Volkswagen debacle) Germany has a reputation for producing high-quality, reliable machinery. The tools themselves might be made in Korea or China.
Example
In Britain, it is common knowledge that Bosch tools are made by a German manufacturer. To a Briton, the name Bosch is very German-sounding: It is about the most German-sounding name you can imagine (for historical reasons concerning WW 1). Britons also think of German tools as being very reliable. A Chinese firm might start selling, Gosch tools. Many English people would see this as German-sounding and so be more likely to buy than if they were called, e.g. Wong tools.
Discussion
If you are manufacturing food, then your product benefits from having an Italian-sounding name.
If you are manufacturing machinery, then your product benefits from having a German-sounding name.
If you are manufacturing fashion accessories, then your product benefits from having a French-sounding name.
If you are manufacturing electronics, then your product benefits from having a Japanese-sounding name.
There is a whole chapter on the importance of brand names having the right sound in terms of nationality in this book, Great Brand Name By Jacky Tai