landsat - Add bands' name and description to the Metadata when stacking using rasterio

I'm using this code, of @Loïc Dutrieux, to stack 8 Landsat bands.

with rasterio.open(final_list[0]) as src0:
   meta = src0.meta

with rasterio.open('stack.tif', 'w', **meta) as dst:
for id, layer in enumerate(final_list):
    with rasterio.open(layer) as src1:

        #the .astype(rasterio.int16) forces dtype to int16

        dst.write_band(id + 1, src1.read(1).astype(rasterio.int16))

When I open the stack.tif with gdalinfo I'm not getting bands' description in the Metadata:

...
Metadata:
AREA_OR_POINT=Area
Image Structure Metadata:
...
Band 1 Block=3596x1 Type=Int16, ColorInterp=Gray
NoData Value=-9999

Band 2 Block=3596x1 Type=Int16, ColorInterp=Undefined
NoData Value=-9999
...

I would like something similar to this:

...
Metadata:
Band_1=Band 1 Reflectance
Band_2=Band 2 Reflectance
Band_3=Band 3 Reflectance

Band_4=Band 4 Reflectance
Band_5=Band 5 Reflectance
Band_6=Band 7 Reflectance
Band_7=Band 6 Temperature
Band_8=Fmask
Image Structure Metadata:
...
Band 1 Block=300x1 Type=Int16, ColorInterp=Undefined
NoData Value=-9999
Band 2 Block=300x1 Type=Int16, ColorInterp=Undefined

NoData Value=-9999
...