Is it obligatory that we praise or send blessings on the prophet Muhammad (saw) every time his name is mentioned?

In a Nutshell: Whilst the issue is disputed amongst the scholars, with some arguing it is obligatory to send blessings on the Prophet (saw) whenever his name is mentioned, and others arguing it is recommended, the strongest position based on all the evidences available to us is it is recommended (mandoub) and not obligatory. Whilst it is not obliged to send blessings upon the Prophet (saw) when his name is mentioned, it is highly recommended and good etiquette for Muslims. It is seen as a bad habit for refusing to do so and a form of miserliness.  Evidences إِنَّ اللَّهَ وَمَلَائِكَتَهُ يُصَلُّونَ عَلَى النَّبِيِّ يَا أَيُّهَا الَّذِينَ آمَنُوا صَلُّوا عَلَيْهِ وَسَلِّمُوا تَسْلِيمًا  Allah and His angels bless the Prophet. O Believers, invoke blessings and peace on him. (Qur'an 33:56) The Prophet (saw) said: "May his nose be robbed in the dust, one in whose presence I am mentioned and he does not send blessings upon me." (Hasan by Tirmidhi, 3545)  The Prophet (saw) said: "The miser is the one in whose presence I am mentioned and he does not send blessings upon me." (Hasan by Tirmidhi, 3546) The Prophet (saw) said: مَنْ صَلَّى عَلَيَّ وَاحِدَةً صَلَّى اللَّهُ عَلَيْهِ عَشْرًا Whoever sends blessings upon me once will have Allah send blessings upon him ten times. (Muslim, 408) The Prophet (saw) said: مَا مِنْ أَحَدٍ يُسَلِّمُ عَلَيَّ إِلَّا رَدَّ اللَّهُ عَلَيَّ رُوحِي حَتَّى أَرُدَّ عَلَيْهِ السَّلَامَ There are none of you who send peace upon me except that Allah returns my spirit so that I can return his greeting of peace. (Abu Dawud, 2041) Juristic Opinions Whilst some scholars argue it is obligatory to send blessings on the Prophet (saw) whenever his name is mentioned, the matter is disputed with others arguing it is recommended and not obligatory. Ibn al-Qayyim is known to have said there was a difference of opinion as to whether it is obligatory to send blessings upon him every time his name is mentioned.  Those arguing it to be an obligation even differ amongst themselves, some arguing: it should be done after every mention, e.g., Fakihani, Tahaawi, Tartooshi, Ibn al-Arabi, al-Haleemi and al-Isfarayini and Ibn Battah  others saying it should be done at least once in a lifetime, e.g., Abu Hanifah, Malik, Thawri and Awza'i with Ibn Abd al-Barr claiming it was the majority view, obligatory in every prayer in the final tashahhud e.g., Shafi'i, Ahmad and others. The position arguing it is obligatory faces the following objections: it concludes using on only some, relevant but, ahadith on the subject, whilst ignoring other evidences that are related to the subject, it ignores the plurality of possible meanings and jumps to a literalist interpretation without a substantive justification why the alternative meanings are not possible Reviewing the matter a little more comprehensively, it appears the ahadith on the subject are using the language rhetorically, not literally, as there are examples of verses, dua, sahabah etc who use the prophet's name with adding anything further. Moreover there are no qara'in to clearly indicate sin even if you were to ignore the additional evidences. Ibn Hajar al-Asqalani's position is the best amongst a range of opinions most of which you have omitted to mention: وَأَجَابُوا عَنِ الْأَحَادِيثِ بِأَنَّهَا خَرَجَتْ مَخْرَجَ الْمُبَالَغَةِ فِي تَأْكِيدِ ذَلِكَ وَطَلَبِهِ وَفِي حَقِّ مَنِ اعْتَادَ تَرْكَ الصَّلَاةِ عَلَيْهِ دَيْدَنًا The scholars responded to those who use these traditions to indicate an obligation by saying that these traditions are rhetorical in confirming and emphasizing sending blessings upon the Prophet, and they are addressed to those who habitually abandon sending blessings upon him. Source: Fath ul-Bari 11/169 Ibn Al-Qayyim adds the additional considerations that indicate it cannot be obligatory: أنه من المعلوم الذي لا ريب فيه أن السلف الصالح الذين هم القدوة لم يكن أحدهم كلما ذكر النبي صلى الله عليه وسلم يقرن الصلاة عليه باسمه وهذا في خطابهم للنبي أكثر من أن يذكر فإنهم كانوا يقولون يا رسول الله مقتصرين على ذلك It is known beyond doubt that the salaf as-salih who are our example, would not send blessings upon the Prophet, peace and blessings be upon him, every time his name is mentioned. This happened a number of times when they addressed him. They would say, "O Messenger of Allah," and limit it to that. Source: Jala Al-Afham 1/393 Conclusion The strongest position on this issue appears to be it is recommended (mandoub) rather than obligatory (fard). Whilst the issue is disputed amongst the scholars, with some arguing it is obligatory to send blessings on the Prophet (saw) whenever his name is mentioned, and others arguing it is recommended, the strongest position based on all the evidences available to us is it is recommended (mandoub) and not obligatory. Whilst it is not obliged to send blessings upon the Prophet (saw) when his name is mentioned, it is highly recommended and good etiquette for Muslims. It is seen as a bad habit of refusing to do so and a form of miserliness.   

My brother or sister Read the Qur'an yourself Surah Ahzab completely. There you will come upon this verse (mafhoom) "And Allah and the Angels send durud upon Muhammad (SAW) so you too o believers send durud upon him" You tell me if Allah and the angels send durud upon him who are we to not say his name with respect. Basically, this is gaining the favor of Allah,you need to get close to Allah by respecting those he loves. That verse has all your answers. Find it yourself in surah ahzab and research it.

no, it is compulsory. once hazrat muhammad(saw) said that the most miser is the one to whom my name is pronounced and he doesn't send me darud i would recommend all to answer all questions in terms of hadith no one is asking their personal opinions