Does anyone know if there is a term to describe the following process?
The two terms of main interest to you
Cellular noise

Cellular noise is random variability in quantities arising in cellular biology. For example, cells which are genetically identical, even within the same tissue, are often observed to have different expression levels of proteins, different sizes and structures. These apparently random differences can have important biological and medical consequences
Cellular noise was originally, and is still often, examined in the context of gene expression levels – either the concentration or copy number of the products of genes within and between cells. As gene expression levels are responsible for many fundamental properties in cellular biology, including cells' physical appearance, behaviour in response to stimuli, and ability to process information and control internal processes, the presence of noise in gene expression has profound implications for many processes in cellular biology.

There is also the term developmental noise.

Developmental noise is a concept within developmental biology in which the phenotype varies between individuals even though both the genotypes and the environmental factors are the same for all of them. Contributing factors include stochastic gene expression and other sources of cellular noise.

Developmental noise is often sounds like a synonym of cellular noise, but it is supposed to include more processes that are causing phenotypic variation then cellular noise. For example, it is common to consider &quot;micro-environmental variation&quot; as being part of developmental noise and not of cellular noise.
The way your phrased your question
In your question you describe only sources of cellular noise. However, you end up saying Hence, cloned organisms are not identical, even if their DNA were identical. I just want to highlight that, there are other reasons than cellular noise for which two clones differ. These include micro-environmental variance, physiological noise, epigenetic variance and macro-environmental variance (often just called environmental variance). Note that I had never encountered the term &quot;physiological noise&quot; before, I just made it up but I wanted to highlight that noise also happen in among cells processes, not only within cells processes.
Intro to quantitative genetics
For a short introduction to quantitative genetics and the different sources of phenotypic variance (genetic variance, environmental variance, developmental noise, etc..) and how the concept of heritability fits into this discussion, please have a look at the post Why is a heritability coefficient not an index of how “genetic” something is?