"Today in history"

"Today in history" is certainly fine, though personally, I would go with "on this day" rather than with "today". I'm not sure why, perhaps I am biased by looking at Wikipedia's front page too often. (This would be actually a non-issue in German, where it's perfectly fine to say "today 150 years ago", "yesterday in two weeks" or "tomorrow three years ago", but I digress.)

As to capitalization, generally speaking, I wouldn't capitalize prepositions in titles (see this question), but it might depend on the context in which your application will be made available. (E.g. if you make it available for a platform or through an app store where all words in titles are capitalized come hell or high water.)

Lastly, as to the name of the app, that's a matter of personal preference, and my guess is as good as anybody's. "Calendar sheet" might work, as might "date sheet", "this day in history" or "tear-off calendar". (Also, I am not a lawyer, so I have no idea whether there might be any legal issues with any particular title.)

The most traditional term for this application is "This day in History".

"Today in History" is perfectly understandable but it sounds just a bit off. "Today" suggests this specific day in time, as in October 1st, 2010 (to use your example)… rather than any October 1st of any year. For example, one would not likely say "Today in 2008…" to mean October 1st, 2008.

The main page of the English language Wikipedia uses "On this day..." but I've also seen "Today in history...". A native speaker should easily understand what you mean. If non-native speakers will be reading your text, I would go with the "On this day..." usage.