What is the ruling on addressing an elderly person as "Hajji" (extending the yaa'), especially if they are not Muslim or have not performed the Hajj pilgrimage?

It is permissible to title someone who has performed Hajj as "Al-Hajj" if there is no fear of conceitedness or showing off from them. The title "Al-Hajj" is also used in some societies for elders as a sign of respect, but it should not be used for someone who has not performed Hajj, as Hajj is a jurisprudential term. It is not permissible to title a disbeliever as "Al-Hajj" because Hajj is an act of worship and obedience to Allah, and it is not permissible to describe a disbeliever with acts of worship. Similarly, the term "Hajji" applies to what applies to the term "Al-Hajj."