In this sentence:
Our professional designers produce high-quality custom logo designs that exhibit the image (that) our clients want to project.
I've added above (that) to the original sentence to denote the point of my concern.
I had guessed this sentence is the compound of two compartment, which are "Our professional designers produce high-quality custom logo designs that exhibit the image" and "our clients want to project (the image)".
Then I had concluded this merge falls into the case of a relative pronoun.
My question is:
Does this omit the relative pronoun?
If it does, is there any formal term that describes this grammatical phenomenon?