You need to use %% in this case. Normally using a ^ (caret) would work, but for % signs you need to double up.
In the case of %%1 or %%i or echo.%%~dp1, because % indicates input either from a command or from a variable (when surrounded with %; %variable%)
To achieve what you need:
move /y "\\myserver\myfolder\file%%20name.txt" "\\myserver\otherfolder"
I hope this helps!