How to override single function of theme's template.php using sub-theme?
It really depends on the type of function:


If it's a theme function (theme_username()) you could simply re-declare the function with your sub-themes name (SUBTHEME_username()).
If it's a preprocess function, you can have your own version of the preprocess in your sub-theme, but IIRC the parent theme preprocess will still be invoked.
If it's a your own function (not a standard HOOK based function), then you would have to put some of your own logic to allow other themes to overwrite it.


Maybe provide some more information on the function in question so that someone can give you a more specific answer.