In the Book of Ruth, when Naomi and the others returned to Judah, how long was this journey and what road did they take? Was there not danger associated with women traveling alone?

The most direct route from Bethlehem to Moab would have taken them by way of the Jericho Road to just north of the Dead Sea, where they could cross one of the fords of the Jordan, then climb back up to the Hill Country of the Amorites and turn south. This would take them to the tableland of Moab, where the land was productive.

On the average, people traveled about 20 miles a day, so that trip would have taken two to three days.

In that society, women traveling along the roads alone were not in any particular danger and were generally not bothered, as to do so went against the ethics of that day. In fact, in these more primitive times, it was safer for women to travel along the roads than it is today in 20th century America.

Why is it that the people of the Bible have no last names?

Actually, in ancient times, both inside and outside the Bible, no one had last names. The concept of last names is of more recent origin, only beginning around the Middle Ages in Europe. It probably became necessary for more detailed identification for tax purposes, etc. But the general idea of last names is merely a few hundred years old and does not date back to ancient times in any society.