If you declare independence, your nation name is bugged.
You can set both the name of your nation and the name of your people when declaring independence.
Once you did that, there are two problems:
1) In the diplomacy and military advisor screens, the name of your people is used to refer to your nation, not the name of your nation
2) A few characters of the people's name that you typed in are removed. This includes non-ASCII characters but also the hyphen and probably more (how to test: Try "Neu-Holländer").
Version: 0.13.0+dev, commit cb10784763ce2a594dc5333ba83a56e197bc4e19.
git.543cfbfa changes the national labels in the places you mention. Unfortunately, the routine that has changed is called in other places, so other things may now break. We shall see.
Confirmed, however this is a very different problem. One issue per bug report please, multiple reports complicate tracking.
I have reposted number 2) into #3306.
I will test if problem number 1) still persists soon. I might repost it in a new bug as well and close this one. (Sadly, I cannot edit the text, apparently.)
Problem number 1) reposted as new bug #3307.
Problem number 2) reposted as new bug #3306.
Please close this bug (#3288) as a (messy) duplicate. Things should be cleaner when this issue has been split into two. (Sorry for the mess, I thought both problems were kinda the same.)