Why does it seems like the convention is Last Name, First Name all over the web?

1. Should names be sorted by first or last name?
2. Why do we alphabetize by last name?
3. Why do they put last names first?
4. When did last names become an appropriate thing?

Should names be sorted by first or last name?

The trivial, most general answer is that sorting by last name makes sense when users are matching based on last names and sorting by first name makes sense when users are matching based on first names.

Why do we alphabetize by last name?

To bypass any ambiguity where someone uses a first name that does not begin with their “official” initial. Me for instance.

Why do they put last names first?

How were surnames chosen? Surnames were originally added to people's first names to distinguish them from other people who had the same first name locally e.g. Robert the baker or Robert at the wood.

When did last names become an appropriate thing?

Family names came into use in the later Middle Ages (beginning roughly in the 11th century); the process was completed by the end of the 16th century.