Since we choose names for our children that are powerful and have meanings and traits behind them that we wish them to show, it makes sense that we would choose names for dogs the same way. Since in Ancient Greek dogs were most likely used for hunting and war we would want them to have names that are powerful and that demonstrate the traits that have.
For those without pets there, typically, is nothing that sense where we include our precious friends in many areas of the pet-owners' life. That is not off topic and was just making a point.
Now, more directly to the named topic, it is human nature to give a name to all in their sight. Humans name their children. their pets and in each case some are more appropriate than others. Ancient Greeks may have been more appropriate than current day as they named all with respect to abilities.
The Ancient Greek practice of picking the best puppy is horrific by today's standards. However, it does have a point.The mother of the litter, would save the strongest and fittest. This is because animals have an innate drive to rescue or choose the fittest, so that their chances of survival is increased.
To the ancient Greeks, picking your new pup was an important decision, just as it is today. Like moderns, the ancients looked for an adventurous and friendly nature, but one test for selecting the pick of the litter seems rather heartless today. Let the mother choose for you, advises Nemesianus, a Roman expert on hunting dogs. Take away her puppies, surround them with an oil-soaked string and set it on fire. The mother will jump over the ring of flames and rescue each puppy, one by one, in order of their merit.