Wizards sure can have some strange names, but there is still a certain logic to them. They are not simply invented out of the aether.
The majority of wizards have fairly normal names, indistinguishable from Bligs, regardless of blood status. Names like Harry, Bob, Dean, or Fred. This is particularly true in the United States.
Some wizards favor more traditional wizard names, which sound quite fanciful to the average Blig. However, even those unusual names are not simply made up. They tend to have a rather "classical" sound, and they always have some root in history, mythology, language, etc. Names like Sirius, Percival, Bartemius, Porpentina, Draco, or Albus are all derivative of some other meaning (usually somehow indicative of some important trait of the character). For example:
- Sirius Black, an animagus that can turn into a large dog, is so named because Sirius is the Dog Star.
- Draco Malfoy is named for a Latin word for dragon or serpent, as he is the series' preeminent Slytherin, and displays many aggressive traits like a dragon.
- Albus Dumbledore's given name is Latin for white, a colour often associated with goodness and purity.
The same is true for surnames. Most sound just like Blig surnames, and while many pure-blood families will try to deny it, the fact is that wizard families are all genealogically connected to Muggle families. There are some more unusual sounding surnames, such as Dumbledore, Hagrid, or Lupin, but these are the exception, and generally have a whimsical sound and a thematic feel to them.
- Dumbledore is an old word for "bumblebee", alluding to Albus Dumbledore busily flitting about the castle humming to himself.
- Lupin is derived from the Latin for wolf, referring to Remus Lupin's lycanthropy.
- Potter is a common surname in England, and refers to the occupation of making pottery, suggesting a simple, down-to-earth family.
It is best to avoid names with a "high fantasy" feel to them, be they given names or surnames. By this, we mean the sorts of names commonly found in Dungeons & Dragons settings, or even Lord of the Rings. The Potterverse has high fantasy elements, but it is a contemporary Earth setting, and ought to feel like one. Some examples of this type of name include: Redblade, Moonstalker, Grinfemmer, Elessar, Nightwind, etc.