Pulliam was arrested without incident early Thursday after a SWAT situation.
The bodies of his alleged victims were found in an apartment near Tramway and I-40 on Tuesday.
In a news conference Thursday, APD released the names of the victims for the first time.
They are Kirsten Landeau and her nephew Dillon Cearfoss. The release of the names confirms what family sources have been telling KOB since the bodies were found.
According to the criminal complaint, Cearfoss was found dead with a wound to the head, sitting on the sofa in the Northeast Heights home he shared with Kirsten Landeau.
A knife was found near his body.
Landeau was found laying on the floor of a bedroom in the same home. She was also bleeding from the head.
A hatchet or axe was found near her body.
Despite that, an autopsy indicates the victims were shot.
According to newspaper accounts, the time Pulliam served for attempted murder stemmed from an incident on Halloween night in 1996, when he and a gang of skinheads beat an Albuquerque man nearly to death.
In 1997, Pulliam was among six men indicted on charges of attempted murder, assault with intent to kill, aggravated battery with great bodily harm, armed robbery, evidence tampering and conspiracy in connection with the attack on the man, Bryan Patterson.
The attack received extensive media attention at the time. Patterson was in a coma for a month and remained hospitalized for several more months.
Stay with KOB for more on this breaking news story.