There are some words in the original Hebrew, Aramaic, or Greek for which there are no exact equivalents in the english language. The Greek word used in John that is often translated to "name"  is one such word.

John chapters 14, 15, 16, and 17 are some of the most remarkable chapters in the entire Bible that describe the kind of relationship God desires. Note the use of the word "name" in these statements.

I will do whatever you ask in My name - Jn 14:13

You may ask me for anything in my name, and I will do it. - Jn 14:14

But the Advocate, the Holy Spirit, whom the Father will send in my name, will teach you all things - Jn 14:26

whatever you ask in my name the Father will give - Jn 15:16

They will treat you this way because of my name - Jn 15:21

my Father will give you whatever you ask in my name. - Jn 16:23

Until now you have not asked for anything in my name - Jn 16:24

In that day you will ask in my name - Jn 16:26

I have manifested Your name to the men - Jn 17:6

Holy Father, keep them in Your namethe name which You have given Me - Jn 17:11

While I was with them, I was keeping them in Your name which You have given Me - Jn 17:12

I have made Your name known to them - Jn 17:26

In the english language, "name" most often refers to a word or phrase by which someone or something can be known.

The original Greek word "onoma" translated to "name" - used in the statements above implies much more than that. It is a figurative expression that means "the manifestation or revelation of someone's character". 

For example, "whatever you ask in My name" is not a "religious formula" just to end prayers or get what we want. According to Hebrew notions, a "name" is inseparable from the person to whom it belongs, i.e. it is something of his essence. So considering this, carefully re-read through the statements above to see if it changes your understanding.