What is the type of ship whose variation of trim will great during listing（heeling）？

No Gonzo, that's not so, it seems that you have no clear idea of the phenomenon we are dealing with. When a boat rotates a certain angle to, say, the X axis, the effects are totally different depending on the origin of coordinates is considered. Therefore, even talking about angles, knowing where the axis of rotation is very important.
For angles, as for distances, nothing is relative, everything must be measured from the proper source, in absolute coordinates, not related. As you well know, because, as you say, you're a designer, the boat shafts that the designer takes to calculate the hydrostatic properties are different from those used to determine the heeling or trim for a load condition.

 

I see
I want to know names of ship whose variation of trim are more than common ship

 

I do not know the name of any ship.
When the aft volume distribution is very different from the bow, trimming while heeling will be more important. Think of a sailboat. for example, with very bulky stern and very thin bow forms.
As Gonzo said, if the hull were a perfect cylinder, there would not be changes in the trim when the boat is heeling.
Analyzes these two possibilities.

 

Angles are not dependent on the origin but the planes only. That is why arbitrary coordinates are routinely used to solve statics and dynamics problem. The offset to the origin does not change the angle between planes, it only translates the relative position. This is a technique learned in elementary classes and universally used. Distances are also relative, since they are measured from an origin. That is the definition of relative values, that they is an arbitrary origin to measure from. If they were absolute, it wouldn't matter where the ship was or what the depth of the bottom was.

 

Seven sentences, none of which has the slightest sense.