Question: I saw most of the Muslims who have completed their Hajj add the prefix `Al-Haj` or `Haji`to their names, like adding `Al-Hafiz` to those who finished memorizing the whole Al-Quran.

> 
> **Haji** is an honorific title given to a Muslim person who has successfully completed the Hajj to Mecca. Women who complete the Hajj
>  are referred to as **Hajiya** - [Wikipedia](https://en.wikipedia.org/wiki/Hajji)
> 
> 
> 

Is it a sunnah or bid'ah?

Answer: 
No brother it's not Bid'ah and not Sunnah. It's a title given to travelers for Hajj, so if you are going to Hajj and I meet you in your way to Hajj I can call you Hajji also you can use it as a title before your name if you has successfully completed the Hajj to Mecca like you said. 

But **it's not bid'ah** because it's just a recipe Arab people used to use it from long time, Just like when I use Al-Hafiz to call the person who finished memorizing the whole Quran, when I use Al-Qari to call the person who read the Quran, when I use Imam to call the leader of a mosque and Muslim community, when I use Shahid to call person who died fighting for Allah Subhanahu wa ta'ala and when I write "Al-Sahabe" before the name of the person who saw the Prophet Mohammad peace be upon him and believed him.

And by the way:
The meaning of Hajj **in Arabic language** can be: "The come" or "pilgrimage" or "intent".
And the meaning of Hajji **in Arabic language** can be: "The comer" or "The pilgrim".

And Allah knows best, Wa salla Allah ala Mohammad.
It's neither bed'a nor sun'a. It is more of honorable name & it can be even used to call those who never been to Hajj to honor them.