C#: How would you make a unique filename by adding a number?

Question

I would like to create a method which takes either a filename as a string or a FileInfo and adds an incremented number to the filename if the file exists. But can't quite wrap my head around how to do this in a good way.

For example, if I have this FileInfo

var file = new FileInfo(@"C:file.ext");

I would like the method to give me a new FileInfo with C:file 1.ext if C:file.ext existed, and C:file 2.ext if C:file 1.ext existed and so on. Something like this:

public FileInfo MakeUnique(FileInfo fileInfo)
{
    if(fileInfo == null)
        throw new ArgumentNullException("fileInfo");
    if(!fileInfo.Exists)
        return fileInfo;

    // Somehow construct new filename from the one we have, test it, 
    // then do it again if necessary.
}

Answer 1

public FileInfo MakeUnique(string path)
{            
    string dir = Path.GetDirectoryName(path);
    string fileName = Path.GetFileNameWithoutExtension(path);
    string fileExt = Path.GetExtension(path);

    for (int i = 1; ;++i) {
        if (!File.Exists(path))
            return new FileInfo(path);

        path = Path.Combine(dir, fileName + " " + i + fileExt);
    }
}

Obviously, this is vulnerable to race conditions as noted in other answers.