Praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
It is established in the authentic Hadiths that the Messenger of Allah (Blessings and peace be upon him) said that he is the master of the children of Adam. This Hadith is reported by Muslim. Indeed, our master Mohammad (Blessings and peace be upon him) has been the master of all people from the time of Adam until the Day of Judgment. Not only this, but he is also the master of the humans, the Jinn, and the angels. Allah The Almighty even criticized those who addressed him familiarly as they would address each other. He the Almighty Said {What means}: "Deem not the summons of the Apostle among yourselves like the summons of one of you to another: God doth know those of you who slip away under shelter of some excuse: then let those beware who withstand the Apostle’s order, lest some trial befall them, or a grievous penalty be inflicted on them." {An-Nur, 63}. He also Said {What means}: "O ye who believe! Raise not your voices above the voice of the Prophet, nor speak aloud to him in talk, as ye may speak aloud to one another, lest your deeds become vain and ye perceive not." {Al-Hujurat, 2}.
It isn`t polite to mention the name of the Prophet (Blessings and peace be upon him) without using proper terms of respect and reverence for him.
As for adding the word "Sayedena/our master in As-Salat Al-Ibrahimya {Allahumma salli 'ala mouhammed, wa 'ala ahli baytih, wa 'ala azwajihi wa dhurriyatih, kama sallayta 'ala ali ibrahim, innaka hamidun madjid, wa barik 'ala muhammed, wa 'ala ali baytih, wa 'ala azwajihi wa dhurriyatih, kama barakta 'ala ali ibrahim, innaka hamidun madjid.}. Scholars have disagreed about this, so there are two opinions about it. The reliable opinion in the Shafie school of thought recommends this addition although it wasn`t mentioned in the version of As-Salat Al-Ibrahimya, which the Prophet (Blessings and peace be upon him) taught to his companions. This is because using this addition means complying with the command to use proper terms of respect for him and this is better than sticking to the aforementioned version of As-Salat Al-Ibrahimya. This view is supported by the fact that Abu Baker refrained from leading the people in prayer because the Prophet (Blessings and peace be upon him) was late due to being busy making reconciliation between disputants. Although the Prophet (Blessings and peace be upon him) told him to lead the people in prayer, he (May Allah be pleased with him) refused and said: "It does not befit the son of Al Quhafa to lead the prayer in the presence of Allah's Messenger (Blessings and peace be upon him)." {Agreed upon}. Another evidence supporting this view is that Ali refused to erase the phrase "The Messenger of Allah" upon writing the Treaty of Hudaybiyyah.
Scholars said that if the Prophet (Blessings and peace be upon him) didn`t teach his companions to say the word "Sayiedena/our master during As-Salat Al-Ibrahimya, we say it out of respect and reverence for him.
Moreover, this slight addition doesn`t invalidate one`s prayer. Therefore, a group of scholars deemed it permissible; they are Al-Iz Ibn Abdulsalam, Al-Karafie, Ar-Ramli, Al-Jalal Al-Mahilli, Kalioby, Al-Sharqawi, Al-Hafsky, Ibn Abdeen, An-Nafrawi, and others. Kindly check Moghni al-Mohtaj, vol.1/pp.384}, {Asna Al-Matalib, vol.4/pp.166} by Zakaria Al-Ansari, {Hasheyat Tohfat Al-Mohtaj, vol.2/pp.88}, and {Al-Mawso`ah Al-Fiqhyah, vol.11/pp.346}.
However, there is another opinion in the Shafie school of thought stating that this addition isn`t recommended.
In conclusion, adding the word "Sayedena/our master" during Tashahud out of respect and reverence for the Prophet (Blessings and peace be upon him) is permissible. Similarly, not adding it is also permissible. This is because both views are based on sound evidence; however, we shouldn`t dispute over this or think ill of each other because of it. There is unanimous agreement on loving, respecting, and revering the Prophet Mohammad (Blessings and peace be upon him). Furthermore, Allah The Almighty Commanded us to be steadfast and united, which is particularly true during these difficult times so as to avoid getting divided and conquered by the forces of evil. And Allah The Almighty Knows Best.