For example, McDowell, or McDonald, or McKenna, etc. Is it necessary to capitalize that letter following "Mc"? And if yes, why is this so?
As Etymology for Mc and O' in names says, Mc is an abbreviation for Mac, and Mac is a Gaelic term meaning "son of". Hence the name McKenna means "son of Kenna", and since Kenna is a proper name, it is capitalized, even when combined with Mac.
(Of course "mac" alone is itself not a proper name, and from one view wouldn't need to be capitalized. However since it is taken as beginning the whole surname, it is capitalized as the initial letter of a proper name. In this respect, it is treated like English most often treats other borrowed prepositions in names, such as de from French and van from Dutch.)
It depends in part on where the person comes from. In Scottish names, the second capital is almost always correct - McDonald, MacDonald, etc (but note that 'Machinery' does need a capital H).
In names of Irish descent, sometimes the owners insist on no second capital; I had a colleague whose surname was Macdonald and he was not happy when the 'd' was capitalized. I'm not sure how general that is.
Some Scottish surnames do not have a capital. Some can be spelt with capital and some without. I was told by a Macintyre, that his name if spelt with the small case i, it meant that historically they were of the lower orders, but the name MacIntyre, with capial I, meant they were of the professional, or I guess landed classes. That's what he told me anyway.