As many people said already, how you communicate will vary greatly depending on the size of the organization and the kind of things they do.

In our case, we work in scrum teams of 5 to 9 people. We work in 2 week sprints. (I apologize in advance for any scrum terminology that might make this confusing. )

Most products are in continuous development, so there are a lot of changes happening very fast.

There is no Data department, the data scientists are integrated into the teams that are developing the product.

This leads to very close communications with the whole team, and specially the product owner. As a result, we have much more informal communication. Whenever we find something worth communication we can just turn our chairs and talk to the PO.

Every other week we have a weekly data update meeting. Mostly powerpoints presented to the rest of the team, to keep everybody on the same page.

For things that need to go higher up, we usually do a report and a presentation. That way the data scientist gets to explain things to avoid confusions and misunderstandings.