Kaiverran nimeni maljakkoon.

Kaiverran is the 1st person singular present tense form of kaivertaa, which means to engrave / to carve.

So:

• kaivertaa = to engrave
• kaiverran = I engrave

The ending -n is the normal marker for I in many Finnish verbs.

Because Finnish often leaves out the subject pronoun when the verb ending already makes the subject clear.

Here, kaiverran already means I engrave, so minä is not necessary.

You could say:

• Kaiverran nimeni maljakkoon.
• Minä kaiverran nimeni maljakkoon.

Both are correct, but the version without minä is very natural and common. Adding minä usually gives a bit more emphasis, like I am engraving it.

Yes, depending on context.

Finnish usually does not have a separate future tense. The present tense often covers both:

• I engrave
• I am engraving
• I will engrave

So Kaiverran nimeni maljakkoon could mean I engrave my name into the vase or I will engrave my name into the vase, depending on the situation.

Because Finnish often expresses possession with a possessive suffix attached directly to the noun.

• nimi = name
• nimeni = my name

Here -ni means my.

So instead of using a separate word like English my, Finnish can attach the meaning directly to the noun.

You can also say:

• minun nimeni = my name

But in many contexts, just nimeni is enough.

This is about the object case.

In Kaiverran nimeni maljakkoon, nimeni is a total object: the action is aimed at the whole name as a complete result. You are engraving your name, not just doing an indefinite amount of engraving.

A learner-friendly contrast is:

• Kaiverran nimeni = I engrave my name / I will engrave my name
• Kaiverran nimeäni = I am engraving my name / I engrave my name in an ongoing, unfinished sense

So nimeni fits well when the sentence presents the action as a whole completed act.

Maljakkoon is the illative case of maljakko.

• maljakko = vase
• maljakkoon = into the vase

The illative case often answers the question into what?

Here it marks the target of the engraving. With a word ending in -o, Finnish typically forms the illative by lengthening the final vowel and adding -n:

• talo → taloon
• maljakko → maljakkoon

Because Finnish often sees engraving as something cut into the material, not just placed on its surface.

So even if English naturally says:

• on the vase

Finnish can naturally say:

• maljakkoon = into the vase

This does not necessarily mean inside the hollow space of the vase. It refers to engraving into the surface/material of the object.

That is a normal stem change for this verb.

The dictionary form is kaivertaa, but the present-tense stem used in forms like I engrave is kaiverra-, so:

• kaiverra-
  • -n = kaiverran

Finnish has a number of verbs that change like this, so the form is something you learn as part of the verb’s pattern. Similar-looking changes happen in other verbs too, for example:

• ymmärtää → ymmärrän
• piirtää → piirrän

So kaiverran is not irregular in a random way; it follows a recognizable Finnish verb pattern.

No, Finnish word order is more flexible than English word order.

Kaiverran nimeni maljakkoon is a natural neutral sentence. But Finnish can move things around for emphasis.

For example:

• Kaiverran nimeni maljakkoon. = neutral
• Minä kaiverran nimeni maljakkoon. = emphasizes I
• Nimeni kaiverran maljakkoon. = emphasizes my name
• Maljakkoon kaiverran nimeni. = emphasizes into the vase

So the order in your sentence is natural, but not the only possible one.

It is grammatically possible, but it is usually not the most natural choice.

That is because nimeni already contains the meaning my. So adding minun is often unnecessary.

Most natural:

• Kaiverran nimeni maljakkoon.

Possible, but usually more emphatic or stylistically marked:

• Kaiverran minun nimeni maljakkoon.

A more normal full version would be:

• Minä kaiverran nimeni maljakkoon.
• Kaiverran minun nimeni, en sinun.
  = I’m engraving my name, not yours.

So minun is mainly useful when you want contrast or emphasis.