  We consider the Brans-Dicke theory in non-metricity gravity, which belongs to
the family of symmetric teleparallel scalar-tensor theories. Our focus lies in
exploring the implications of the conformal transformation, as we derive the
conformal equivalent theory in the Einstein frame, distinct from the minimally
coupled scalar field theory. The fundamental principle of the conformal
transformation suggests the mathematical equivalence of the related theories.
However, to thoroughly analyze the impact on physical variables, we investigate
the spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker geometry,
defining the connection in the non-coincidence gauge. We construct exact
solutions for the cosmological model in one frame and compare the physical
properties in the conformal related frame. Surprisingly, we find that the
general physical properties of the exact solutions remain invariant under the
conformal transformation. Finally, we construct, for the first time, an
analytic solution for the symmetric teleparallel scalar-tensor cosmology.
