It is unclear, however it seems to have been bestowed upon the position.
While no other information exists in the other canon Tolkien works (yes I searched them all), we can make some headway from the information that is given. Some of the below requires slightly more imagination than others, but for the most part it should follow reasonably.
Firstly, we must note that the Shire was given certain privileges by Aragorn:
King Elessar issues an edict that Men are not to enter the Shire, and he makes it a Free Land under the protection of the Northern Sceptre.
Return of the King - Appendix B
The Northern Sceptre was the Sceptre of Annúminas, the only surviving sceptre from Númenor, which was the symbol of office for the Lords of Andúnië. It was held by the Kings of Arnor and represented the Sceptre of Númenor, which was lost with Ar-Pharazôn in the Blessed Realm.
The role of the Counsellor of the North-kingdom serving the Northern Sceptre seems to reflect that of the "Council of the Sceptre", which were represented by the six regions of Númenor and guided the King but held no power.
In a note on the ‘Council of the Sceptre’ at this time in the history of Númenor it is said that this Council had no powers to govern the King save by advice; and no such powers had yet been desired or dreamed of as needful. The Council was composed of members from each of the divisions of Númenor; but the King’s Heir when proclaimed was also a member, so that he might learn of the government of the land, and others also the King might summon, or ask to be chosen, if they had special knowledge of matters at any time in debate.
Unfinished Tales - Aldarion and Erendis: Note 23
Given that at the time, of the Free Peoples in North Western Middle-earth, the majority of Men (or related) were the Hobbits of the Shire it follows that the leaders of the Shire were given positions on the council.
The original quote itself gives us some insight into whether it was personal or part of the position. The edict gave the honour of "Counsellors of the North-kingdom" to the positions of each as opposed to the person. Furthermore, given that Sam was up for re-election (and that meaning the role could've gone to someone else) when Aragorn announces the edict, it would seem to be part of the position.
King Elessar makes the Thain, the Master, and the Mayor Counsellors of the North-kingdom. Master Samwise is elected Mayor for the second time.
Return of the King - Appendix B
As such, I feel it is safe to conclude that the honour was bestowed upon the positions of Mayor, Thain and Master, however there is no strictly conclusive evidence to suggest this was the case.