I'm going to take a stab at it being Steven Brust's Vlad Taltos series. There are fourteen published novels, each named after a Great House (which indeed sound like dragon names), the first of which, Jhereg, is named after his pet dragon's species.
Vlad Taltos is one of the human minority (known by Dragaerans as "Easterners"), which exists as a lower class in the Empire. Vlad also practices the human art of witchcraft; "táltos" is Hungarian for a kind of supernatural person in folklore. Though human, he is a citizen of the Empire because his social-climbing father bought a title in one of the less reputable of the 17 Dragaeran Great Houses. The only Great House that sells memberships this way is, not coincidentally, also the one that maintains a criminal organization. Vlad proves surprisingly successful in this organization. Despite being a human and a criminal, he has a number of high-ranking Dragaeran friends, and often gets caught up in important events.
- Jhereg (1983)
- Yendi (1984)
- Teckla (1987)
- Taltos (1988)
- Phoenix (1990)
- Athyra (1993)
- Orca (1996)
- Dragon (1998)
- Issola (2001)
- Dzur (2006)
- Jhegaala (2008)
- Iorich (2010)
- Hawk (2014)
And there is indeed a character named "The Necromancer".
The Necromancer is an undead demon that was sent by the Gods in the Halls of Judgment to aid Sethra Lavode and Her Majesty, Zerika the Fourth reestablish the Dragaeran Empire as well as defend Dragaera from the Jenoine. She chose to remain with Sethra thereafter.
WillAdams noted in a comment that this specifically sounds like the plot for Athyra.
Vlad has traveled through Dragaera for over two years. He now wears normal clothing, has discarded most of his assassin arsenal, and has lost a finger. While entering the village of Smallcliff, he meets Savn, a Teckla boy apprenticed to the local physicker. The two strike up a brief conversation, and Savn is often confused by Vlad's behavior, as he has never seen an Easterner before. Vlad's arrival in town is concurrent with the mysterious death of Reins, a former servant of the Baron of Smallcliff.
Vlad shows up again at the local inn, causing a stir. He talks to Savn and becomes interested in Reins's death. While most of the village assumes that Vlad killed Reins, Vlad begins to believe that the death did have something to do with him. After some questioning, Vlad determines that the Baron of Smallcliff is still Loraan, an Athyra wizard he killed during the events of Taltos. The time Savn spends with Vlad in public alienates him from his friends in the village.
Savn takes Vlad to some nearby caves at his request and begins learning about witchcraft, sorcery, and thinking for himself. Vlad tells him that Loraan is an undead necromancer who killed Reins to draw Vlad out for a Jhereg assassin. Savn also becomes acquainted with Vlad's two jhereg, who are on constant lookout for assassins. Recurring sections from the point of view of Rocza reveal that she obeys the "Provider" only out of obligation to her mate, Loiosh.
