For  - The word translated as "for" can be treated as supporting a dependent clause, or, in written English, as "this is because..." to start a new sentence.

where -- The word translated as "where" demonstrative pronoun ("this" "that"), but it often acts as a pronoun ("the one that), especially a connective pronoun ("the one that") introducing a dependent clause. In the previous verse, Matthew 18:19, the word translated here as "where" was translated as "that." However, this form here (genitive) becomes the adverb "where" when referring to the subject as it does here.

two -- The Greek word for "two" means "two" or a "couple." 

or -- "Or" is translated from a Greek word that means primarily "or" but serves as "than" in a comparison.

three - "Three" is the Greek word that means the number three.

are  - (CW) This seems to be a helping verb that indicates the present tense of the following verb, but it is an active verb here, not a helping verb.

gathered  - (WT, WF) "Gathered" is from a verb that means "to bring together," "join," "collect," "unite," and "gather together." It is a play on the verb in the previous verse, Matthew 18:19, that comes from the same root that means "come to an agreement" or "share an opinion." Jesus usually uses this term to be bringing people together, but sometimes uses it for gathering crops. The form is a participle, that is, a verbal adjective.  The tense is past perfect, complete in the past.

together-- This is from the prefix of the previous verb that means "together."

in -- (CW) The word translated as "in" means, with the accusative object used here, it means "into," "on," and "for."  This is not the preposition usually used with this phrase. This could be better translated as "for" to distinguished the meaning here.

my . --  "My" is the regular first-person pronoun in Greek in the possessive form, so "my" or "of me." 

name, The Greek word translated as "name" is much more complicated than it might at first appear. It can simply mean a "name" as in English, but this can be many things in Greek. It doesn't mean the thing itself, but what people call it. For example, it can mean a "false name," or "a pretense" as we say "this is a marriage in name only." It can also mean representing another person's authority, as we say, "he is acting in the name of the boss." See this article.

there  - "There" is a word meaning "there," "in that place," and in philosophy means "the intelligible world."

am -- The verb "is" here is the common form of "to be" in Greek. It means to have a certain characteristic or remain in a certain condition. It also equates terms or assigns characteristics.

I -- This is from the first-person, singular form of the verb.

in -- The word translated as "in" means "in," "within," "with," "during" (time),  or "among"  with a dative object as the one here. 

the -- (IW) There is nothing that can be translated as "the" in the Greek source.

midst  - The word translated as "midst" generally means "middle" but has a lot of special meanings with different prepositions. One of those with "in" is "offer for competition" and "middle point." It also means "difference."

of -- This word "of"  comes from the genitive case of the following word that requires the addition of a preposition in English.  The most common is the "of" of possession.

them.  - -- The word translated as "them" is the Greek word commonly translated as third-person pronouns in English.