HP Quiz -This isn't MAGIC, it's LOGIC ;) -Season 3 - Page 18

I have two names, one opposite to another

Apparition is also called as disapparition (to disappear) w.r.t a person at the starting place and Apparation (to appear) w.r.t a person at the destination. Both names are opposites.

Alas, both make sense, so why bother

These names are based on the point of view of someone at a place, start or destination, so both make sense

I am popular with Wizards of age

It is a popular method of travel specially with young ones who passed the Licence test..

But most prefer my counterparts at any stage

Most of the witches and wizards prefer other methods such as broomsticks, floo powder or portkeys..

Lack of haste with me gives them success

One of the 'D's is deliberation/lack of haste that is essential for successful apparition

While failure causes them distress

This method is tricky and most often cause splinching when not performed correctly

So make sure to know about me fully

Self-explanatory

For knowledge about me is imparted for a fee

The apparition classes are given by a ministry wizard and cost some galleons

P.S.-Edited last line of the riddle - isn't given freely is changed to is imparted for a fee...thanks lumos 🤗