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I saw most of the Muslims who have completed their Hajj add the prefix Al-Haj or Hajito 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
Is it a sunnah or bid'ah?
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.
