I just got the titular staff and it appears to summon a melee-type Dremora Kynreeve every time I use it. Will this ever change?
The Sanguine Rose is unique among conjuration staves in that the spell scales with level. So while the effect is the same (a melee Dremora, in Daedric Armor wielding a Daedric Weapon), the actual level of the summon increases as the Dragonborn gains in power.
I finally found some more precise data. Even though the staff is unobtainable before level 14 in a normal game, there are appropriately leveled Dremora for that range.
Level Dremora Summoned 1 Dremora Churl 12 Dremora Caitiff 19 Dremora Kynval 27 Dremora Kynreeve 36 Dremora Markynaz 46 Dremora Valynaz [sic]
The Rose summons a Dremora Kynmarcher, Dremora Valkynaz or a Dremora Markynaz to fight for the Dragonborn 60 seconds.
It does change - it will summon either a Dremora Kynreeve, Dremora Valkynaz or a Dremora Markynaz when you use it. source: Elder Scrolls wiki