In enemy phase，if all the damages were assigned to an asset（such as Leather Coat），can I trigger its ability to attack the enemy？The rule said that when you were dealt damages，first assign，then apply. So even if damages were dealt to an asset，it also meant that “I was dealt damages”.

Yes, you can trigger Survival Knife in that case - for exactly the reasons that you mentioned (damage dealt to you can be assigned to assets controlled by you) 🙂 .

Think of it as all the damage is being assigned to your investigator first, before being assigned by you (or by certain card effects) to the various assets your investigator (or in certain cases other investigators) controls

So the damage dealt to "you" triggers the Survival Knife for sure

Be careful about using "assigned" and "dealt" interchangeably (though it sometimes is, as with Guard Dog).

"Dealing Damage/Horror" is the entire process.
"Assigning" them is the act of determining what cards will get how many units.
"Applying" is when the damage/horror is actually put on the card.

Some cards trigger when damage/horror is dealt (e.g. I've Had Worse) and some trigger when it's assigned (e.g. Armor of Ardennes). Triggering "when dealt" will resolve before triggering "when assigned".

Survival Knife triggers *after* damage is dealt, so it is assigned and applied before Survival Knife resolves. But all of it is "dealt to you", which is why it can trigger, regardless of where it is assigned. Even if it all gets assigned to someone else's card (e.g. True Grit), it was still dealt to you, so Survival Knife is still valid (on the other hand, I do not believe the owner of True Grit can trigger their own Survival Knife, as the damage was not dealt to that investigator).