Yes, that is true. But remember God loved him more for his heart. So personally I think that not naming your son Esau because of the outcome of Esau from the bible would be a waste. Since Esau is such a good name. Besides, in the end Esau and Jacob made it right with each other. And Esau was very blessed.
This is a pretty interesting Biblical name, one of the many names from the Bible which is never used anymore. The ultra-Orthodox defamation of the character of Esau has always made me very uncomfortable, since, if you just read the straight text and not the later extra-Biblical books of commentary and imagined stories, Esau is at worst impulsive and uncouth. He's nowhere near the arch-villain and anti-Semite he later turned into in apocryphal writings. It's probably too much to hope for, though, that the names of wrongly villified characters in the Bible be reclaimed by more than a few people.
There are a couple famous tongue-twisters about Esau, all with pretty much the same theme:
I saw Esau Sitting on a seesaw. I saw Esau; He saw me.
"I saw Esau" was also a Top 100 song for The Ames Brothers in 1956. It's based off the tongue-twister, and Esau ends up being sawed off the seesaw for sitting there with the singer's girlfriend.