Symbol for dyadic rationals Set of integers is denoted by the symbol $\mathbb Z$, $\mathbb Q[x]$ stands for univariate polynomials over rationals, etc. Is there a symbol which indicates the set of dyadic rationals?

I don't believe there is a widespread symbol. Your best bet is to just define your terms, e.g. 'let $D$ denote the set of all dyadic rational numbers'.

The dyadic rationals are the localisation of $\mathbb{Z}$ with respect to the powers of $2$ (or equivalently by the set $\\{ 2 \\}$), and also the free $\mathbb{Z}$-algebra generated by the set $\\{ 2^{-n} \mid n \in \mathbb{N} \\}$, so any of the following will do: $$\mathbb{Z}[2^{-1}], \quad \\{ 2 \\}^{-1} \mathbb{Z}, \quad \mathbb{Z}[x]/\langle 2x-1 \rangle, \quad \mathbb{Z} \langle \\{ 2^{-n} \mid n \in \mathbb{N} \\} \rangle$$