I believe that demonofthemist is very close.
Building on and branching out from his answer, you are:
A verb in English.
At the risk of getting too technical,
you are the infinitive form of a regular verb in English.
Your three friends are:
The three tenses of verbs (past, present, and future).
When I meet the first, he usually sends me two letters.
The past tense of a regular verb in English is formed by appending “ed”.
For example: “ask” → “asked”, “answer” → “answered”
(Note that I mentioned “regular” verb.
There are “irregular” verbs that do not follow this rule.
the two verbs in the above sentence from the OP are both irregular:
“meet” → “met”, “send” → “sent”)
When I meet the second,
she tends to leave me just as I am, sometimes having passed me a letter.
The present tense of a verb in English is usually the base/root/infinitive,
but an “s” gets appended when it is used with third-person singular subject.
For example : I type, you type, he types
A few irregular verbs don’t follow this pattern; for example,
I am, you are, he is; I have, you have, he has
When I meet the third, he presents me with his final testament.
The future tense of a verb in English is (almost?) always formed
by adding the auxiliary word “will”.
For example : I will type, you will type, he will type
The legal document specifying how a person’s estate should be distributed
after he dies is called a “last will and testament” (emphasis added).
Alternatively, it could be that you are
and your “friends” are
the ghosts of Christmas past, present, and future. :-)