I recently encountered a way to distinguish these that I thought was rather elegant:
direct product/sum - $A \otimes B$, $A \oplus B$
Kronecker product/sum - $A \hat{\otimes} B$, $A \hat{\oplus} B$
So, for example, $I_3 \hat{\otimes} B = B \oplus B \oplus B$ clearly shows this specific Kronecker product is expressed in terms of direct sums.
However, the hat on the Kronecker product is not strictly necessary, unless there is a desire for consistency with the way the Kronecker and direct sums are distinguished using this method.
Reference:
Chirikjian, G. "Stochastic Models, Information Theory, and Lie Groups, Volume 1: Classical Results and Geometric Methods. Applied and Numerical Harmonic Analysis." (2009)
I found this reference on Google Books when searching for "kronecker sum" vs "direct sum". I had not seen this notation or anything like it in the dozen or so other references I've encountered, so it caught my attention. In most references, it is usually explained in the adjacent text which sum is meant. (Not that you asked, but to be complete I will mention that the products are less important to distinguish, since it is clear from the definitions of the symbols which product is meant. If the symbols represent matrices or vector spaces, then the symbol means Kronecker or direct product, respectively.)
At least in Belgium, high schoolers get taught that $n \in [a, b]$ is the standard notation for a given range of real numbers, so I wouldn't use it straight away. As others have pointed out though, introducing it beforehand is probably the best way to go from a practical standpoint. In my personal opinion, "Let $x \in \mathbb{N} \cap [a, b]$" is the least ambiguous but to people who grew up with $[a, b]$ it'll probably come over as convoluted.
Best Answer
I don't know how popular this is but I've seen the convention: $$[n]\equiv\{1,2,3,4,\ldots n\} $$
See for example: http://www.math.cmu.edu/~lohp/docs/math/mop2013/combin-sets-soln.pdf