Policista zná moji totožnost, ale moje občanství je neznámé.

Because the possessive pronoun můj / moje / má has to agree with the noun it belongs to in gender, number, and case.

• totožnost is feminine singular, and here it is in the accusative because it is the direct object of zná
• občanství is neuter singular, and here it is in the nominative because it is the subject of je neznámé

So the pronoun changes shape:

• moji totožnost = feminine accusative singular
• moje občanství = neuter nominative singular

• totožnost is in the accusative singular because znát takes a direct object: the policeman knows my identity
• občanství is in the nominative singular because it is the subject of je neznámé: my citizenship is unknown

A useful shortcut:

• after a verb like zná, ask what does he know? → moji totožnost
• before je neznámé, ask what is unknown? → moje občanství

Because neznámé is agreeing with občanství, which is neuter singular.

The dictionary form is neznámý = unknown, but adjectives change their endings:

• masculine: neznámý
• feminine: neznámá
• neuter: neznámé

So:

• občanství je neznámé means the citizenship is unknown

Yes. Mou totožnost is also correct, and many learners are taught that form first.

With possessive pronouns like můj, Czech often allows both a shorter and a longer form:

• mou / moji
• mé / moje

So all of these are possible:

• mou totožnost
• moji totožnost
• mé občanství
• moje občanství

In practice:

• the shorter forms can sound a bit more formal or compact
• the longer forms are very common in everyday language

Czech usually distinguishes between znát and vědět:

• znát = to know someone/something, to be familiar with
• vědět = to know a fact, to know that...

So:

• Policista zná moji totožnost = the policeman knows my identity
• Policista ví, kdo jsem = the policeman knows who I am

Both can express similar ideas, but they are built differently. In this sentence, znát fits naturally with the noun totožnost.

These are useful patterns:

• nouns ending in -ost are very often feminine
  Example: radost, možnost, totožnost
• nouns ending in -ství are usually neuter
  Example: město? no, different pattern, but dětství, občanství, přátelství

So:

• ta totožnost → feminine
• to občanství → neuter

Knowing the gender helps you choose the right adjective and pronoun endings.

Because some Czech nouns referring to male people end in -a but are still masculine animate.

Policista belongs to that group, like:

• turista
• kolega
• předseda

So even though the ending looks feminine at first, the noun is masculine because it refers to a man:

• ten policista

This is a very common learner trap.

Because Czech does not use articles like English does.

So:

• policista can mean a policeman or the policeman
• the exact meaning comes from context

In this sentence, English might say either:

• The policeman knows my identity... or
• A policeman knows my identity...

Czech leaves that unstated unless the context makes it clear.

Not completely. Czech word order is more flexible than English word order.

The version here is neutral and clear:

• Policista zná moji totožnost, ale moje občanství je neznámé.

But other orders are possible for emphasis:

• Moji totožnost policista zná, ale moje občanství je neznámé.
• Policista moji totožnost zná, ale moje občanství je neznámé.

The basic meaning stays the same, but the emphasis shifts. English usually cannot move things around this freely.

It is grammatical, but it sounds fairly formal and a bit official.

That is mostly because of the nouns:

• totožnost = identity
• občanství = citizenship

These are words you often hear in legal, police, or administrative contexts.

In everyday speech, people might choose simpler or more personal phrasing depending on what exactly they mean. But for an official-style sentence, this one is perfectly fine.