Repute, n.
1. Character reputed or attributed; reputation, whether good or bad; established opinion; public estimate. He who regns Monarch in heaven, till then as one secure Sat on his throne, upheld by old repute. Milton.
2. Specifically: Good character or reputation; credit or honor derived from common or public opinion; -- opposed to disrepute. "Dead stocks, which have been of repute." F. Beaumont.
1 other Webster entry under this spelling
Repute (r-pt), v. t. [imp. & p. p. Reputed; p. pr. & vb. n. Reputing.]
To hold in thought; to account; to estimate; to hold; to think; to reckon. Wherefore are we counted as beasts, and reputed vile in your sight Job xviii. 3. The king your father was reputed for A prince most prudent. Shak.
Shades of meaning
Fernald has no entry of its own for repute; he lists it under fame.
Where he writes about it:
Repute is a somewhat formal word, with the same general sense as reputation. — from character
Reputation and repute are more limited than fame, and may be either good or bad. — from fame
Notoriety is evil repute or a dishonorable counterfeit of fame. — from fame