Merhaba.

Is this only my impression or the man who narrates this story:

https://www.youtube.com/watch?v=c8qnfHLYnJw

pronounces "Nasreddin" in the story´s title (around 0:08) as [Nasettin] ??

Is this a kind of simplified pronuciation?

No, it is a mis pronounciation.

I thought so too is sounded like nesretdin but it could be that he was just to close to the microphone

Nesrettin is possible....

Nasreddin is also a Arabic noun clause. Nasr´ed-din.

nasr means "help" in Arabic

din means "religion"

Literally it means help of religion. But when I look for a translation I only found this one: helper of the religion. So instead of nasr it must be nasir. Nasir means helper in Arabic.