The Mujahideen Division Khandaq was associated with MILF and obviously Islam. They exist as a pseudo name for the Moro Islamic Liberation Front so as not to endanger the political deception the MILF were perpetrating against the Filipino government. It is not unlike the PLO/PA/Fatah wearing the Aqsa Martyrs' Brigades label when they terrorize and the other name when they extract political concessions.
The Mujahideen Division Khandaq has asserted that its attacks are a show of "solidarity" to Muslim militants in the Mindanao province of the Philippines. In their public relations releases, the Mujahideen Division Khandaq has actually claimed to be a splinter group of MILF based in Kuala Lumpur.
The invocation of "Khandaq" in the group's name is a reference to the historical Battle of Khandaq or the Trench during Islam's formation. In this failed siege, the Meccan merchants who had been repeatedly terrorized and robbed by Muhammad and the first Muslims went to Medina to put an end to the violence but they were thwarted by a ditch dug in the sand.