In The Strang Case of Dr. Jekyll and Mr. Hyde, Mr. Utterson is very concerned with Dr. Jekyll's reputation as Stevenson's novella moves toward the disgraceful conclusion. Dr. Jekyll is concerned for his reputation to an extreme degree from the beginning of his career in medicine. In Victorian England, indeed in much of the history of Western civilization, once a person lost their reputation through some criminal act or some deep moral flaw or religious failing, there was no way to reclaim it.
Now society honors the idea of meritocracy: you rise or fall--and rise again--on merit. As a result, someone who has failed in life can claim a second chance and do better and reclaim the good and honorable public opinion that a virtuous person is rewarded with. In Victoria England, such reclamation, such a second chance was not possible: regaining your good standing as a person of worth and value in the community wasn't an available option.
Take Oscar Wilde as an example, after serving his sentence for his conviction, none but one friend made contact with him; he lived quietly in Europe; and died ill, poor and alone. A person's reputation, which is comprised then and now of moral values, trustworthiness, abiding by the law, providing financially for oneself and family, meant being welcomed at social engagements, a wide circle of friends and business associates, broader choices for a marriage partner, friends and family.
For Dr. Jekyll, since he was involved in borderline and then full-fledged criminal activity, loss of reputation meant public trial and conviction and, after the grizzly murder, execution. Since religion was more universally embraced in the Victorian era then now, reputation also included religious beliefs and practices. Since much of what Dr. Jekyll did in his research and as Hyde was irreligious, his reputation could also be doomed to a life with no medial patients, family, friends or opportunities if he were denounced as a man devoid of religion.