His reputation has been tarnished – what should he do?

You should note that it has been proven that the Prophet
(peace and blessings of Allaah be upon him) said: “How wonderful is the
affair of the believer, for it is all good, and this does not apply to
anyone except the believer. If something good happens to him, he gives
thanks for it and that is good for him, and if something bad happens to him
he bears it with patience and that is good for him.” Narrated by Muslim,
2999. This hadeeth indicates that all the believer’s affairs are good,
because he alternates between gratitude and patience, and there is reward in
both.  

You should also note that the best of people, the Messengers
(peace be upon them) were slandered by their enemies. Allaah says
(interpretation of the meaning): 

“Likewise, no Messenger
came to those before them but they said: ‘A sorcerer or a madman!’”

[al-Dhaariyaat 51:52]

Even our Prophet (peace and blessings of Allaah be upon
him) was slandered by his enemies and accused of being a sorcerer or a
madman. 

Indeed, things got so bad that the hypocrites impugned his
honour, but despite that he bore it all with patience and sought reward from
Allaah, and he put his trust in Allaah. 

“And whosoever fears Allaah and keeps his duty to Him, He
will make a way for him to get out (from every difficulty).

3. And He will provide him from (sources) he never could
imagine. And whosoever puts his trust in Allaah, then He will suffice him.
Verily, Allaah will accomplish his purpose”

[al-Talaaq 65:2-3]

So you have to be patient and seek reward with Allaah, and
remember that this is one of the means by which Allaah expiates your sins. 

You have the right to defend yourself and establish your
innocence of whatever you are accused of, and to denounce as liars those who
accuse you of that; this is not regarded as the kind of gheebah (backbiting
or gossip) that is forbidden. Allaah says (interpretation of the meaning): 

“Allaah does not like that the evil should be uttered in
public except by him who has been wronged”

[al-Nisa’ 4:148]

If you can confront the
one who has accused you and advise him and exhort him to fear Allaah, that
is good. Perhaps he will give up what he has been doing and that will be a
cause of his repenting and following the straight path. Or you could send a
wise person to do that.

 You have to avoid situations and places that may cause doubts and suspicion, because that person may take them as a means to confirm his suspicions. You have to be patient and turn to Allaah, calling upon Him, and Allaah will grant you relief from what you are facing.  And Allaah knows best.