As people generally use the word "honor" they do not do so in the context of thinking about moral virtue. As a result they often confuse honor with fame.
A virtuous person is an honorable person, a person who ought to be honored by the community in which he or she lives. But the virtuous person does not seek honor, being secure in his or her own self-respect. Lack of honor does not detract from the efficacy of moral virtue as an operative factor in the pursuit of happiness -- as a means to leading a good human life.
Virtuous persons may be considered fortunate if their virtue is recognized and publicly applauded.
Being honored for one's virtue is gift of good fortune, and like other gifts of fortune, not being honored is not a major obstacle to living well, as are poverty, loss of liberty, or loss of health.
These other goods of fortune are rightly desired by virtuous persons who recognize them as goods not entirely within their own power to achieve, as moral virtue itself is. Although this statement is true of honor also, virtuous persons may enjoy being honored while they're still alive instead of after they are dead: but they are under no moral obligation to seek it. They may think themselves dishonored if other persons do not give them the respect that accords with their own self-respect.
The public distribution of honors (as for example in the Queen's list in England) is thought to be one of the chief problems in distributive justice. For those who hold that honor and fame are distinct in principle, justice does not require fame to be proportionate to the possession of moral virtue.
Persons lacking moral virtue can achieve fame as readily as, or perhaps more easily than, those who have a high degree of moral virtue. Fame belongs to the great, the outstanding, the exceptional, without regard to their virtue or vice.
Infamy is fame, no less than good repute. The great scoundrel can be as famous as the great hero. There can be famous villains as well as famous saints. Existing in the reputation a person has, regardless of his or her accomplishments, fame does not tarnish as honor does when it is unmerited.
We normally desire the esteem of our fellow human beings, but is not this wish for the esteem of others a desire for fame rather than for honor? Virtuous person will not seek fame or be unhappy for lack of it. For fame can be enjoyed by bad men and women, as well as good. When it is enjoyed by virtuous persons without being sought by them, it is not distinguishable from honor, for then it is deserved.
In a constitutional government, those who hold public office exercise more power than ordinary citizens who are not elected or appointed to administer government. But such power is vested din the political offices they hold, as defined by the Constitution, not in them personally. It is only personal power over others, competed for in worldly ventures, which is an object of wrong desire, and one which no virtuous persons would seek. Machiavelli's "Prince" sets forth the rules by which this kind of wrong desire may be realized.
Adler's Philosophical Dictionary (1995)
Great Ideas from the Great Books (1963)
by Mortimer J. Adler