for /f "tokens=2 delims=_" %%G in ('dir /b dirname') do @echo %%G

set dirname="relevantdir"
for /f "tokens=1,2 delims=_" %%G in ('dir /b %dirname%') do rename %dirname%%%G_%%H %%H

powershell
ls "*_*.txt" | %{mv -confirm:$false $_.name ($_.name).split("_")[1]}