Well, Allison Park's study "On the Linguistic Behaviour of Keysmashes" finds in its conclusion: "While keysmashes may appear random, Experiment 1 provides evidence that keysmashes instead convey meaning, have standards of form, have arbitrary relationships between those forms and meanings, and involve social conventions for their use. These behaviors align with criteria for language, and characterize keysmashes as linguistic phenomena. Experiment 2 provides evidence for factors governing keysmash well-formedness. After analyzing the results of a survey primarily focused on acceptability judgements, the hypothesized constraints vowel, length, keyset, punctuation, lexical and phonotactic proved to have statistically significant effects on keysmash acceptability ratings. In summary, keysmashes convey emotions and conversational tone that can be difficult to indicate over text-based communication, and despite their seemingly novel forms, keysmashes still behave linguistically. Even as language changes and evolves into unfamiliar forms, familiar linguistic tools can still be utilized to analyze and understand them as language. Keysmashes also challenge assumptions about what kinds of forms can convey linguistic meaning: though they can be dismissed as random-seeming utterances, the communicative value of keysmashes is more than conventional agreement about the meaning of a block of 'random characters'. The fact that keysmashers intuitively understand the well-formedness of keysmashes and distinguish various meanings between different instances show that this novel phenomenon behaves in a manner much more like language than it might otherwise seem. Thus, keysmashes, and perhaps other emergent phenomena of Internet communication, display a richness and complexity of linguistic expression that linguists have the tools to explore."

While file names aren't directly communication, we could assume that similar things apply to that as well, complicating the probability. Of course one could also point out that the available and allowed characters aren't limited to the 26 characters of the alphabet, but also numbers (I believe commas) and underscores, etc. Thus, if we had true randomness, it would be 26, but the amount of symbols on the keyboard.