Η εταιρεία έχει καλή φήμη.

Because εταιρεία is a feminine noun in Greek. You can see that from the article η, which is the feminine singular form of the.

Greek nouns have grammatical gender, so even things like company are masculine, feminine, or neuter. Here:

• η εταιρεία = the company
• feminine singular

This is grammatical gender, not biological gender.

Because the subject is η εταιρεία = the company, which is third person singular: it / she in grammatical terms.

The verb έχω = I have is the dictionary form.
In this sentence you need the he/she/it has form:

• έχω = I have
• έχεις = you have
• έχει = he/she/it has

So Η εταιρεία έχει... means The company has...

Greek often leaves subject pronouns out when they are not needed, because the verb ending already shows the person and number.

So Greek normally says:

• Η εταιρεία έχει καλή φήμη.

and not something like:

• Η εταιρεία αυτή έχει... unless you want extra emphasis

English needs it has, but Greek usually does not need a separate it.

Because adjectives in Greek must agree with the noun they describe in gender, number, and case.

Here, φήμη is:

• feminine
• singular
• accusative singular as the object of έχει

So the adjective must also be feminine singular accusative:

• καλός = masculine
• καλή = feminine
• καλό = neuter

That is why Greek uses καλή φήμη.

It is functioning as the direct object of έχει, so it is accusative.

However, with many feminine nouns like φήμη, the nominative and accusative singular look the same in modern Greek:

• nominative: η φήμη
• accusative: τη φήμη

Without the article, the noun itself stays φήμη, so you identify the case from its role in the sentence.

Because Greek often leaves the article out when talking about something in a general or indefinite way, especially after verbs like έχω.

So:

• έχει καλή φήμη = has a good reputation

This is very natural Greek.

You could also say:

• έχει μια καλή φήμη

but that sounds more like has a certain good reputation or has one good reputation, and it is less neutral here. The version without μια is the most natural choice.

Yes. Greek word order is more flexible than English, although the basic order here is very natural:

• Η εταιρεία έχει καλή φήμη.

You could also hear:

• Καλή φήμη έχει η εταιρεία.

That version gives more emphasis to καλή φήμη.

So the original sentence is the neutral, standard order:

• subject + verb + object

Roughly as eh-teh-REE-ah.

A more detailed breakdown is:

• ε = eh
• αι = e
• εί / ει = ee
• final α = ah

So εταιρεία sounds like eh-teh-REE-ah, with the stress on REE.

It can mean both, depending on context.

Common meanings include:

• reputation
• fame
• renown

In this sentence, καλή φήμη most naturally means good reputation, not fame.

So although φήμη has a wider meaning, the phrase here strongly points to reputation.

No, that would not be natural Greek.

Greek normally uses έχω for this idea:

• Η εταιρεία έχει καλή φήμη. = The company has a good reputation.

Using είμαι με... would sound unnatural here. So if you want to express that someone or something possesses a reputation, έχει is the normal verb.

Only because it is at the beginning of the sentence, so it is capitalized.

• Η εταιρεία... at the start of a sentence
• η εταιρεία... in the middle of a sentence

It is the same word: the feminine singular definite article, the.