The Islamists seized the town of Mubi in Adamawa state last week and now insist it be called Madinatul Islam, or "City of Islam" in Arabic. Gwoza in neighbouring Borno state which was captured in July is now being called Darul Hikma or "House of Wisdom", multiple residents said.
Boko Haram's leader, Abubakar Shekau, in a video released in August declared that he had made Gwoza part of a caliphate -- an announcement that recalled a similar move by the Islamic State militant group which has taken over parts of Iraq and Syria.
The extremists are believed to control more than two dozen towns and villages in Nigeria's far northeast and there are signs that they are trying to advance south towards Adamawa's capital Yola.
"They have given new names to Gwoza and Mubi, which they say are now part of their Islamic state," said Ahmad Maishanu, who fled Mubi with his mother on Wednesday to Yola.
Tijjani Kalifa, who left Mubi on Monday and has contacts in Gwoza, also reported that Boko Haram was forcing people in both towns to use the new names.
Both witnesses said all the churches in Mubi had been burnt down and that Islamists were patrolling the streets regularly, with no sign of resistance from the security services.