Let's open with a truism: assuming proper balance, the more classes are different from each other, the better. So here's a suggestion to really distinguish necro pets from other pet classes. It's a small nerf in one way, but an enhancement in another, and -- if one thinks through all the implications -- it not only distinguishes the necro, but adds some interesting mechanics.
The change: summoning a pet requires not only a component, but a fresh corpse -- target a dead mob, and your summon transforms it into your pet. And when your pet dies, it transforms back into a corpse. This builds on the archetype of the 'necro' - 'mancer' ... one who controls the dead.
Gamewise, this has interesting ramifications. On the plus side, if your pet dies, you can loot it to recover items you've given it (summon weapons, etc). On the downside ... you need a corpse to start. If your pet dies in combat, this normally isn't a problem -- use the corpse of the old pet. It only comes into play if you fail to resummon your pet before the old corpse expires. Then you'll need to either have your group kill a mob for you, find one low enough for you to solo ... or, in true Frankensteinian fashion, wander around and grave-rob the corpse from another player or group. What could better fit a necro?
An advanced version might allow you to modify (slightly) the attributes of your pet based on what mob type you chose as starter corpse. Animate a mob with high magic resist but low cold/fire resists, and you get a pet with those attributes, or a pet resistant to slashing damage, but vulnerable to blunt weapons, etc. There's really a lot of room to expand upon this.