Yes, it's very widely used. Hence many possibly related posts out there, but since this question is focused on a specific point, here is an answer tailored to this question:
it means "saying that" or "it is called"
Exactly. And for this question we focused on the "it is called" version.
but sometimes it seems to have another nuance.
In this case, it's not that a third nuance was added. It's more like "you have to open your eyes to increase the scope of the it is called". The key is, "called" can be used for a wide array of nuances. See following example:
でも, それは 後悔 という 切実な 形を とる ことも なく
Let's trim this poetic phrase down to: 後悔 という 切実な形.
It's saying: "切実な形 of which I am talking about 後悔". Not the best translation, but it may help you notice talking about is interchangeable with the word call in English too:
- You committed a crime called robbery
- You committed a crime BTW I'm talking about robbery
- You committed a robbery という crime
In conclusion, という here is still basically "it is called", and "called" has many nuances in its own. They may be interpreted as:
- 切実な形 which is called 後悔
- 切実な形 known as 後悔
- 切実な形 i.e. 後悔
- 切実な形 which I describe as 後悔
- 切実な形 - BTW I'm talking about 後悔