Υπογράφω δήλωση υιοθεσίας για να υιοθετήσω και καταχωρίσω ζώο.

Because Modern Greek usually does not use an infinitive the way English does.

In English, you say:

• to adopt
• to register

In Greek, the usual pattern is:

• για να + verb

So για να υιοθετήσω και καταχωρίσω ζώο means in order to adopt and register an animal.

A helpful way to think about για να is:

• για = for
• να = marker that introduces the subjunctive clause

Together, they often mean so that / in order to.

They are in the form usually called the aorist subjunctive in learner-friendly explanations.

After να (and therefore after για να), Greek uses the subjunctive, not the indicative.

So:

• να υιοθετήσω
• να καταχωρίσω

do not mean past tense here.
They describe actions as single, complete events.

That is why this form fits well with the idea of purpose:

• sign the form
• so that I can complete the adoption
• and complete the registration

If Greek wanted to emphasize an ongoing or repeated process, it would use the present/imperfective form instead.

Because υπογράφω is the main verb of the sentence, while υιοθετήσω and καταχωρίσω are inside a purpose clause.

So the sentence has two parts:

• Υπογράφω δήλωση υιοθεσίας = the main statement
• για να υιοθετήσω και καταχωρίσω ζώο = the purpose

υπογράφω is in the present indicative, meaning something like:

• I sign
• I am signing

But after για να, Greek switches to the subjunctive. That is why the forms look different.

Greek often leaves the indefinite article unstated.

So a bare noun can mean:

• δήλωση υιοθεσίας = an adoption declaration/form
• ζώο = an animal

Greek does have words like:

• μια δήλωση
• ένα ζώο

but they are not always necessary.

This is especially common in:

• formal language
• bureaucratic language
• general statements

So the sentence is understandable without explicitly saying μια or ένα.

Literally, it means declaration/form of adoption.

Breakdown:

• δήλωση = declaration, statement, form
• υιοθεσίας = of adoption

The word υιοθεσίας is in the genitive singular of υιοθεσία.

Greek often uses:

• noun + genitive noun

where English might use:

• a compound noun
• or of
• or an adjective

So:

• δήλωση υιοθεσίας = adoption declaration
• literally declaration of adoption

Because in Greek, when two verbs are coordinated, one να can govern both of them.

So this is fine:

• για να υιοθετήσω και καταχωρίσω ζώο

It is also possible to say:

• για να υιοθετήσω και να καταχωρίσω ζώο

Both are grammatical.

For many learners, the repeated version feels clearer because English repeats to less strictly but Greek learners often like seeing the pattern more explicitly.

So:

• να + verb + και + verb = acceptable
• να + verb + και να + verb = also acceptable

It is understandable, but many native speakers would probably make it slightly more explicit.

For example:

• Υπογράφω μια δήλωση υιοθεσίας για να υιοθετήσω και να καταχωρίσω ένα ζώο.

That version sounds a little more natural to many learners because it includes:

• μια = a
• ένα = an
• a repeated να

But the original sentence is still structurally clear, especially in a formal or administrative context.

καταχωρίσω means something like:

• register
• record officially
• enter into a system/database/file

It is a fairly formal verb and often appears in administrative or official contexts.

So in this sentence it does not just mean mention or write down casually.
It suggests an official act of registration.

That makes it a good fit if the context is paperwork, adoption records, or animal registration.