Evidenční známka patří k psovi s mikročipem.

In this context, evidenční známka means something like an identification tag, registration tag, or official dog tag.

• evidenční = relating to records, registration, or official identification
• známka = mark, badge, tag, token, stamp, etc., depending on context

So together, it is not just any tag, but an official tag connected with registration/record-keeping.

Because Czech does not use articles the way English does.

So Evidenční známka can mean:

• a registration tag
• the registration tag

Which one is meant depends on the context. English forces you to choose; Czech usually does not.

There are three important case forms here:

• Evidenční známka = nominative
  This is the subject of the sentence.

• k psovi = dative
  The preposition k requires the dative case.

• s mikročipem = instrumental
  The preposition s meaning with requires the instrumental case.

So the structure is:

• subject: the tag
• relation: belongs/goes with
• target: to the dog
• description of the dog: with a microchip

Because pes is the basic dictionary form, but after k you need the dative case.

The noun changes like this:

• pes = dog
• psovi = to the dog

So:

• pes = nominative
• k psovi = to/toward/with respect to the dog

This is also slightly irregular, because pes changes its stem to ps- in many forms.

Yes. The dative singular of pes can be psovi or psu.

However:

• psovi is very common and often clearer for learners
• psu is shorter and also correct

So both are grammatical, but psovi is a very normal choice here.

Here patří k means belongs with, goes with, or is assigned to.

That is a bit different from plain patřit někomu:

• Známka patří psovi = The tag belongs to the dog.
• Známka patří k psovi = The tag goes with that dog / is associated with that dog.

In administrative or official language, patří k can sound a little more like is linked to or corresponds to.

Because s meaning with requires the instrumental case.

The noun changes like this:

• mikročip = microchip
• s mikročipem = with a microchip

So -em is the instrumental ending here.

It describes the dog.

So the meaning is:

• k psovi s mikročipem = to the dog with a microchip

In other words, this is basically a shorter version of:

• k psovi, který má mikročip = to the dog that has a microchip

The context makes it clear that the dog has the microchip, not the tag.

Yes, you pronounce it.

The noun pes changes stem in many forms:

• pes
• psa
• psovi
• psi

So the p is not silent. The beginning of psovi is pronounced like the ps- in English psst, followed by -ovi.

This kind of stem change is normal for some Czech nouns.

Yes. Czech word order is relatively flexible because the case endings show the grammatical relationships.

The given sentence is a neutral, natural order:

• Evidenční známka patří k psovi s mikročipem.

But you could also say:

• K psovi s mikročipem patří evidenční známka.

That version puts more emphasis on the dog with the microchip.

So the word order can change, but the emphasis changes too.