The word "name" translates from the Hebrew word sheem, which designates something as a mark or memorial of individuality, and by implication, honor, authority, or character. The King James Version (KJV) also translates it into "fame," "famous," "infamous," "named," "renown," and "report."
From this verse, we see that a good name (a combination of reputation and character) certainly should outweigh riches, prominence, position, and status. Conversely, a lack in either can leave us in a state of moral and/or spiritual poverty, seeking self-worth over godly worth.
An example of this can be seen in those who strive for political office or a promotion. They attempt to leave an impression of character with the public or a boss, but it is an impression built on a shaky foundation of duplicity. While they may have a "good" reputation, it is not supported by the real important ingredient, character, which is earned throughout our lives.
A starkly contrasting example of this is that of Jesus Christ as a man: "[He] made Himself of no reputation, taking the form of a bondservant, and coming in the likeness of men" (Philippians 2:7). Christ—God Himself—humbled Himself, surrendering His right to a godly reputation, yet still left the legacy of righteous character and reputation as a human.
Ecclesiastes 7:1-8 gives another example of a good name, this time compared to that of fine ointment and life and death. The chapter starts with "A good name is better than precious ointment," but goes on to say "the day of death [is better] than the day of one's birth." Ointment, in this case, symbolizes a richness or excellence that is added to a person's state, or it may represent anointing oil used to set a person or thing apart as different or special. Verse 8 concludes, "The end of a thing is better than its beginning, and the patient in spirit is better than the proud in spirit."
In human terms, we know at birth we are a clean slate—we have no knowledge, understanding, wisdom, reputation, or character. Only at death, after lifelong endeavor, do we have the total life experiences to establish a good or bad name and reputation, and this occurs because of the character we have gained or failed to gain in the process.
For those who truly desire it, a good reputation and godly character are built patiently and not through devious or self-aggrandizing means. Based on this, reputation or a perceived good name is simply not enough without the character to accompany it.