Should we flatten the graves and remove any visible marks which indicate the deceased name and lineage?

It is permissible in the Islamic law to build over the graves of the friends of Allah [Ar. Awliya'] and scholars in order to mark them, maintain their upkeep and visit them as well as seek blessings. This is based on the hadith narrated by Kathir ibn Zayed al-Madani from Al-Muttalib who said:

"When 'Uthman ibn Maz'un died, he was brought out on and buried. The Prophet (peace and blessings be upon him) ordered a man to bring him a stone, but he was unable to carry it. The Messenger of Allah (peace and blessings be upon him) went and rolled up his sleeves [to carry the stone]. The narrator Kathir told that al-Muttalib remarked: The one who told me about the Messenger of Allah (peace and blessings be upon him) said: I still seem to see the whiteness of the forearms of the Messenger of Allah (peace and blessing be upon him) when he rolled up his sleeves. He then carried the stone and placed it at the head of the deceased saying: “I am marking my brother's grave with it and I shall bury those of my family who die beside him" [Abu Dawoud; and Al-Hafidh ibn Hajar declared that it has a fair chain of transmission).

Imam al-'Ayni said in Sharh al-Sunan (6/157): "the hadith implies rulings on: permissibility of marking graves with stones and the like; permissibility to gather one's deceased people in one grave . It is also a proof for using sign boards, nowadays, at the head of graves to mark them".

Al-Bukhari reported from Sufyan al-Tammar that he had seen the grave of the Prophet (peace and blessings be upon him) elevated and convex.

In his Musanaf, ibn Abu Shaybah reported through Imran Ibn Abu 'Ataa who said: I have witnessed the funeral procession of Ibn 'Abbass. Ibn Al-Hanafiyya has pitched a tent over his grave [to receive consolation for three days).

He also reported through Muhammad ibn al-Munkadir that 'Umar (may Allah be pleased with him) constructed a tent over the grave of the mother of the believers Zainab bint Jahsh (may Allah be pleased with her).

Actions of the (Salaf) ancestors
The pious predecessors of the Muslim community and their followers have observed [building over grave] until it became unanimously approved. Domes and mosques have been built over the graves of the four imams—Abu Hanifa, Malik, al-Shafi'i and Ahmed (may Allah be pleased with them) as well as other scholars and righteous people of different times and places.

The Rulings on Building over Graves and the Conditions therein:
Jurists maintain that if building over a grave is done out of mere extravagance, it is then disliked to do so. If the grave was endowed for the cause of Allah, it is then unlawful to build over it, because it may incur restrictions upon people. However, it should be noted that it is only permissible to build over the grave with the purpose of marking and recognizing it or if the grave was a private property.

The Shafi' scholar, imam al-'Umrani said in al-Bayan: "If the grave was a private property, then it is permissible to build over it whatever one wishes, because it does not incur restriction upon others. If otherwise—i.e. the grave was endowed for the cause of Allah, it is not permissible to build over it."
The Hanbali scholar ibn Muflih said in al-Fru': "the author of al-Mustaw'ib and al-Muharar stated: “If the grave is a private property, there is no objection to having a dome, house or a sitting place over it—because it is permissible to conduct burials in this way.

He said in al-wasila: it is disliked to have a luxurious building over a grave—such as a dome—i.e. there is no objection to have an adjunct building in order to always mark the grave and keep it in shape, since it takes the same ruling of putting stones [at the head of a grave to mark it).

He said in al-Fusul: if the grave is a private property, it is then permissible to have building over it. However, if the grave is endowed for the cause of Allah, it is then disliked to have buildings over it. It will incur restrictions and divert the grave from the job for which it was constructed." 

Relieving Some Contentions
The hadith that Imam Muslim and others reported from Jabir ibn Abdullah (may Allah be pleased them) in which he said: "The Messenger of Allah (PBUH) forbade that the graves should be plastered (made into permanent structures), used as sitting places (for the people) or building over them" is directed to whoever constructs something over the grave out of mere extravagance and not for marking it.

In addition, the hadith that Muslim reported from Abu al-Hayaj al-Assdi that 'Ali ibn Abu Talib (may Allah be pleased with him) said to him: "Shall I not send you on a mission on which I was sent by Allah's Messenger (peace and blessings be upon him) "Do not leave any image without erasing it, nor any elevated grave without leveling it to the ground" refers to the graves of the disbelievers as he combined between images and the disbelievers graves. However, the graves of Muslims can be left elevated and should not be leveled to the ground as it had previously mentioned with the case of the grave of the Prophet (peace and blessings be upon him) and the act of many righteous predecessors.

Based on this and in reference to the question, it is permissible in Islamic law to build over graves—as long as the grave was not made for the cause of Allah or the building is made for the purpose of extreme extravagance.