I'm a native English speaker and the names in Crime and Punishment were difficult for me as well. Russian nicknames often sound completely different from the original name (ex: Avdotya -> "Dunya"). What helped me was keeping a bookmark with the names and a brief description of each character and referring to it frequently.

Sparknotes has a character page, but there are some spoilers on it, so I've copied and pasted a mostly spoiler-free version below and added some extra clarification. Some spoilers were unavoidable because they're so crucial to understanding the characters, but I don't know how far in the book you are, so I put some phrases behind spoiler tags.

Rodion Romanovich Raskolnikov (“Rodya,” “Rodka”) : The protagonist of the novel.

Sofya Semyonovna Marmeladov (“Sonya,” “Sonechka”) : Raskolnikov’s love and Semyon Marmeladov’s daughter.

Avdotya Romanovna Raskolnikov (“Dunya,” “Dunechka”) : Raskolnikov’s sister. Most often referred to as "Dunya."

Arkady Ivanovich Svidrigailov : Dunya’s (Raskolnikov's sister's) depraved former employer.

Dmitri Prokofych Razumikhin : Raskolnikov’s friend, a poor ex-student.

Katerina Ivanovna Marmeladov : The consumptive wife of Semyon Marmeladov.

Porfiry Petrovich : The magistrate in charge of investigating>! the murders!<.

Semyon Zakharovich Marmeladov : An alcoholic public official whom Raskolnikov meets at a tavern. Father of Sofya/"Sonya" and married to Katerina. Most often referred to by his last name, Marmeladov.

Pulcheria Alexandrovna Raskolnikov : Raskolnikov’s mother.

Pyotr Petrovich Luzhin : Dunya’s (Raskolnikov's sister's) fiancé.

Andrei Semyonovich Lebezyatnikov : Luzhin’s (Raskolnikov's sister's fiance's) grudging roommate.

Alyona Ivanovna : An old, withered pawnbroker >!whom Raskolnikov kills!<.

Lizaveta Ivanovna : Alyona Ivanovna’s sister.

Zossimov : Raskolnikov’s doctor and a friend of Razumikhin (Raskolnikov's poor student friend).

Nastasya Petrovna (“Nastenka,” “Nastasyushka”) : A servant in the house where Raskolnikov rents his “closet.”

Ilya Petrovich (“Gunpowder”) : A police official whom Raskolnikov encounters >!after committing the murder!<.

Alexander Grigorievich Zamyotov : A junior official in the police station who suspects that >!Raskolnikov is the killer!<.

Nikolai Dementiev (“Mikolka”): A painter who is suspected of >!being the murderer!<.

Polina Mikhailovna Marmeladov (“Polya,” “Polenka,” “Polechka”) : The oldest daughter of Katerina Ivanovna Marmeladov from her former marriage.