The reason why it is so called:

Ibn Faaris said in Mu’jam Maqaayees al-Lughah (p. 445):

The letters Ra’, jeem and ba’ form a root which indicates supporting and strengthening something with another thing. … Hence the phrase “Rajabtu’l-shay’” means I venerated it… It was called Rajab because they used to venerate it, and it is also venerated in Sharee’ah.

The people of the Jaahiliyyah used to call Rajab Munassil al-Asinnah [the one that causes the sharp heads of weapons to be taken off], as it was reported that Abu Rajaa’ al-‘Ataaridi said:
We would a rock, then if we found a better rock we would throw the first one aside and adopt the other. If we could not find a rock, we would make a pile of dirt, then we would bring a ewe and milk it over the pile of dirt, then we would do tawaaf around it. When the month of Rajab came, we would say Munassil al-Asinnah [the one that causes the sharp heads of weapons to be taken off], and we would not leave any spear or arrow that had an iron piece in it but we would take the metal head off and put it aside during the month of Rajab. (Narrated by al-Bukhaari).

Al-Bayhaqi said: the people of the jaahiliyyah used to venerate these sacred months, especially the month of Rajab, and they would not fight during this month.