You don't need a template. It's free form. Give it a title that makes sense: eg. "Explanation - Name mismatch between Birth Certificate and Passport". One short paragraph with fact/issue. One short paragraph sentence saying what you can / cannot do, eg "This mismatch is common in [country] and does not require name change, the name in [passport] is considered official and used and supported consistently in other documents."
General common sense: short, factual, minimal long explanations; you don't need the extraneous 'letter' format stuff (to whom it may concern, address, etc - not needed), it will be part of a package. Simple letters of explanation that address a specific issue, separately from others, are easier to digest and use. (Eg four separate LOEs for distinct issues with appropriate simple titles, don't make them search for explanations in a longer document about multiple things).
I do not think a cover letter makes sense generally unless there is some overall issue / background that is necessary to understand in multiple areas (eg occurs in multiple areas / multiple subsections of the application). An example of that might be deficiencies in documentation of cohabitation because some country has a cumbersome official registration procedure that doesn't work for unmarried couples (so official address confirmation not possible). But you have to use your judgment on whether your specific situation presents such issues.
Good luck.
