All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
It is permissible to use the nickname “Hajji” and call someone who performed Hajj with it unless the person does so to show off. An-Nawawi said: “They (the scholars) agreed that it is desirable to use the name that a person likes, for example Abu Bar As-Siddeeq’s real name was ‘Abdullaah Ibn ‘Uthmaan and his nickname was ‘Ateeq, and also Abu Turaab was the nickname of ‘Ali Ibn Abu Taalib.”
Therefore, it is permissible to use a name if the person likes to be called with it and there is no religious prohibition in it.
Calling a person “Hajji” was not known during the era of the Prophet ; however, this does not prevent from using it as other names and nicknames that were not used at that time. This is not among the forbidden innovations as it has no link with worship or getting closer to Allaah; rather, this is among the customs and worldly affairs of the people.
Allaah Knows best.