Though it doesn't follow your described logic directly, a different train of thought towards logical deduction to the existence of God is called Intelligent Design.
"The theory of intelligent design holds that certain features of the
universe and of living things are best explained by an intelligent
cause, not an undirected process such as natural selection. Through
the study and analysis of a system’s components, a design theorist is
able to determine whether various natural structures are the product
of chance, natural law, intelligent design, or some combination
thereof. Such research is conducted by observing the types of
information produced when intelligent agents act. Scientists then seek
to find objects which have those same types of informational
properties which we commonly know come from intelligence. Intelligent
design has applied these scientific methods to detect design in
irreducibly complex biological structures, the complex and specified
information content in DNA, the life-sustaining physical architecture
of the universe, and the geologically rapid origin of biological
diversity in the fossil record during the Cambrian explosion
approximately 530 million years ago." [
The theory of intelligent design basically says that the existence of things such as DNA (which is essentially a data storage mechanism) is not explained by natural selection, and goes directly against the second law of thermal dynamics, which as some science text books state: "The entropy of the universe increases in all natural processes." Which essentially means that any system, which is a closed system, will always move away from order and towards chaos. Intelligent design then holds that existence of things like DNA are better explained by the existence of an intelligent creator.
When I saw the posted question without it's description, this is what I thought you were referring to. I understand now, that you were looking for a different train of logic, but I think that others may stumble across this, and be looking for the name for Intelligent Design, so I thought to post here, since it is another answer for a "name behind a concept of believing in God based on logical deduction."