  We consider a renormalization group approach based on the idea that the
primary contribution to the Schwarzschild-like black hole spacetime arises from
the value of the gravitational coupling. The latter depends on the distance
from the origin and approaches its classical value in the far zone. However, at
some stage, this approach introduces an arbitrariness in choosing an
identification parameter. There are three approaches to the identification: the
modified proper length (the Bonanno-Reuter metric), the Kretschmann scalar (the
Hayward metric), and an iterative, and, in a sense, coordinate-independent
procedure (Dymnikova solution). Using the WKB method, we calculated grey-body
factors for the Standard Model massless test fields and their corresponding
energy emission rates. For all of these solutions, we found that the intensity
of Hawking radiation of massless fields is significantly suppressed by several
or more orders once the quantum correction is taken into consideration. This
indicates that the effect of suppression of the Hawking radiation may be
appropriate to the quantum corrected black holes in asymptotically safe gravity
in general and is independent on the particular choice of the identification
parameter.
