You can't use a filename like iexplore by itself because the path to internet explorer isn't listed in the PATH environment variable for the system or user.
However any path entered into the PATH environment variable allows you to use just the file name to execute it.
System32 isn't special in this regard as any directory can be added to the PATH variable. Each path is simply delimited by a semi-colon.
For example I have c:\ffmpeg\bin\ and c:\nmap\bin\ in my path environment variable, so I can do things like new ProcessStartInfo("nmap", "-foo") or new ProcessStartInfo("ffplay", "-bar")
The actual PATH variable looks like this on my machine.
%SystemRoot%\system32;C:\FFPlay\bin;C:\nmap\bin;
As you can see you can use other system variables, such as %SystemRoot% to build and construct paths in the environment variable.
So - if you add a path like "%PROGRAMFILES%\Internet Explorer;" to your PATH variable you will be able to use ProcessStartInfo("iexplore");
If you don't want to alter your PATH then simply use a system variable such as %PROGRAMFILES% or %SystemRoot% and then expand it when needed in code. i.e.
string path = Environment.ExpandEnvironmentVariables(
@"%PROGRAMFILES%\Internet Explorer\iexplore.exe");
var info = new ProcessStartInfo(path);