Chassidim calling Rebbes G-d Alter Rebbe's Bio Avigdor's accusation

B"H

ואין לתמוה אם ניצוץ מהארת שכינה, נקרא בשם שכינה
There is no need to wonder at a spark of the radiance of the Shechinah being referred to (in Tzavaat HaRivash) as Shechinah.

דהא אשכחן שאפילו מלאך נברא נקרא בשם ה׳, בפרשת וירא, לפירוש הרמב״ן

For we find that even a created angel, which is not a spark of the Shechinah, is referred to by G‑d’s Name in Parshat VaYeira, in the verse,59 “And he said, ‘Lord, do not pass by your servant,” according to the commentary of R. Moses Nachmanides (the Ramban);

וכמו שכתוב: ותקרא שם ה׳ הדובר אליה וכו׳, וכהאי גוונא טובא

and as it is likewise written,60 “And [Hagar] called the name of G‑d Who spoke to her...,” where we are explicitly told that we are speaking of an angel; and many more [passages] like this.

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http://www.chabad.org/library/article.asp?AID=7970
The above quote is referenced in a footnote in the biography of the Alter Rebbe

http://store.kehotonline.com/index.php?stocknumber=EAR-RABB.H&deptid=&parentid=&page=1&itemsperpage=10

the 1st Rebbe of Chabad as an explanation as to why Chassidim sometimes call their Rebbes G-d which was one of the accusations against them.
(The Biography was compiled by Rabbi Nissan Mandel and edited by the Rebbe King Moshiach himself. It was published by Kehot main Chabad Lubavitch publishing house almost 40 years ago and has since been republished a number of times with this passage and footnote left in.)
See here:

6.In some passages of the book of the Karlinists the terms "thought",speech", and "vitality" are used to personify the Creator. This is contrary to the Jewish faith. Moreover ,they write that a person may sometimes be in unity with the Creator,hence they call their Rabbis "G-d."

Note that in his accusation against the Chassidim quoted above Avigdor calls them Karlinists because at that time Karliner Chassidim were popular in that area and this term was used regarding Chassidim in general.

It's explained in the Midrash commenting on Yeshiahu (Issiah) 52 that King Moshiach (Messiah) will be exalted even above angels thus it shouldn't be surprising that he too is called by G-d's name.

Rabbi Mordechi Eliyahu, the past Chief Rabbi of Israel after his visit to the Rebbe said. "I saw that no secret is hidden from him, and I mean that simply and explicitly. He knows all of the Talmud, Poskim (legal precedents) and in the Mystical works his understanding is VERY VERY deep. He is the master of light. He is a master of all the Torah. And is an expert on everything that is happening in Israel. His face shines like an angel of G-d and he himself is higher than any angel. He is the greatest Torah master in our generation and no one is even close to him. And together with this he worries for every Jew in the world."

(Post in progress check back later)