Anglii was the Roman name for the place we now know as Denmark, at least the southern part. The occupants did not like it there so they sailed west and found an island to live on. The part that is called England on that island gets its name from them.
Not to put too fine a point on it, but “Anglii” isn’t the name of the place, but the tribe. However, it derives from the Germanic name for their territory. There are two possible etymologies.
One is that the name comes from the root of the modern German word “eng”, “narrow”, which might make sense, since it’s on the narrow neck connecting the upper part of the Danish peninsula to the mainland.
The other is that it comes from the root of the English “angle”, “a bend”, which also survived in German and English as a word for fishing and a fisherman. The territory of the Angles was a river estuary, and that source might make sense, too.
In any case, the Romans heard the Germanic name of the place, and called the people who lived there, the “Anglii”.
It’s on the Baltic side of the neck of the Danish peninsula, by the way.