Your example of the name 'Rashid Ghani', where you say that 'Ghani' means 'rich', just sounds like a personal name to me, either given or assumed.
The word 'epithet' is really defined as "an adjective added to a person's name or a phrase used instead of it". Examples from history would include "William the Conqueror", or "Ivan the Terrible", who gained these epithets by reputation. Modern examples might include sportspersons such as William "The Refridgerator" Perry, who I believe was so-called because of his physical stature.
In direct answer to your question, unless this word meaning 'rich' directly describes the person, then I'd have to say no - it is not an 'epithet', even if it derives from some adjective or title. Epithets are normally earned through actions and reputation.
In western cultures, there are many surnames that derive from historic professions, statuses and the like. For example, occupations like Baker and Cooper (someone who makes barrels) are common surnames today, likely handed down through generations from an ancestor who actually did those jobs. If someone named 'Baker' today was by trade a baker, this would likely be a coincidence, unless the trade had stayed in the family for centuries. So, these are not 'epithets', even though they may have derived from one. Similarly, given names (forenames) that have meanings are not really epithets, because the person may not live up to them!
I am aware that, in some cultures, people take on new names at various stages in their life which may reflect a change in status. Even so, unless they directly describe the person in a unique, identifying way, rather than just a generic title that means they are a husband or a wife, for example, then I would still argue it is not a true epithet.