Yes, it’s true!
die Bedeutung is the German word for meaning and deutsch is the German word for, well, german.
The origin is the old root *teuta- which simply meant tribe, folk. So the Germans essentially decided to call themselves “folk”.
And the root is also the origin of the verb deuten. It can mean interpret and also point at, but at its core is about the idea of making the people, the tribe understand something. And that’s why Bedeutung means meaning. Just think of a heavy thunderstorm and how tribes would have tried to interpret that. Like… why is Thor angry? What did we do? What is Thor trying to tell us?
The family of deuten is pretty interesting, so if you want to learn more and see some examples, then check out this article on YourDailyGerman: