How does DateTime.Now.Ticks exactly work?

Not really an answer to your question as asked, but thought I'd chip in about your general objective.

There already is a method to generate random file names in .NET.

See System.Path.GetTempFileName and GetRandomFileName.

Alternatively, it is a common practice to use a GUID to name random files.

The resolution of DateTime.Now depends on your system timer (~10ms on a current Windows OS)...so it's giving the same ending value there (it doesn't count any more finite than that).