How do I determine the owner of a process in C#?

You can use WMI to get the user owning a certain process. To use WMI you need to add a reference to the System.Management.dll to your project.

By process id:

public string GetProcessOwner(int processId)
{
    string query = "Select * From Win32_Process Where ProcessID = " + processId;
    ManagementObjectSearcher searcher = new ManagementObjectSearcher(query);
    ManagementObjectCollection processList = searcher.Get();

    foreach (ManagementObject obj in processList)
    {
        string[] argList = new string[] { string.Empty, string.Empty };
        int returnVal = Convert.ToInt32(obj.InvokeMethod("GetOwner", argList));
        if (returnVal == 0)
        {
            // return DOMAIN\user
            return argList[1] + "\\" + argList[0];
        }
    }

    return "NO OWNER";
}

By process name (finds the first process only, adjust accordingly):

public string GetProcessOwner(string processName)
{
    string query = "Select * from Win32_Process Where Name = \"" + processName + "\"";
    ManagementObjectSearcher searcher = new ManagementObjectSearcher(query);
    ManagementObjectCollection processList = searcher.Get();

    foreach (ManagementObject obj in processList)
    {
        string[] argList = new string[] { string.Empty, string.Empty };
        int returnVal = Convert.ToInt32(obj.InvokeMethod("GetOwner", argList));
        if (returnVal == 0)
        {
            // return DOMAIN\user
            string owner = argList[1] + "\\" + argList[0];
            return owner;       
        }
    }

    return "NO OWNER";
}