Why was the letter “Hai” added to Avraham's name?

Question

Avarham Avinu was originally Avram - and Hashem added the letter Hai to his name and changed it to Avraham. Why from all letters was the letter Hai added?

Answer 1

The name אברם numerically equals 243. Originally Avram was master of 243 of his 248 body parts: all except his two eyes, two ears, and male organ. [These are usually exposed to improper stimuli, even against a person's will.] However, with the Hei (numerical value of 5) added to his name, Hashem granted him control even over these [so that he no longer could see or hear anything that he shouldn't].

(Nedarim 32b and Tosafos there)

Answer 2

From some basic Googling found:

Abram = exiled father

Abraham = father of multitudes

Seems the meaning of the words also changed. So that would explain why "Hai."

Answer 3

The Ham alludes to hamon. So like yydl said, he has become a "father of multitudes" - Av hamon. The reish stays because Hashem wants to add to Avrahams name, not subtract. (Ibn Ezra). Rashi adds that Avram alludes to being the father of just Aram.

Answer 4

I recall hearing a while back that as Sarai became Sarah - the Yud switched into a Hei. The remaining 5 went to Avraham. I do not recall the source.