Anatomically speaking, could an aquatic mammal develop a horizontal fin that instead of being localized at the end of the tail extends up the sides in a similar manner to how an eel's fin extends up the top and bottom? Particular concerns are whether some sort of rigid support is necessary for that sort of fin and if so, what it would come from in a mammal. For that matter, do any mammals have enough vertebrae to make anguilliform swimming practical?
EDIT: I seem to have misunderstood the point of the question the first time round. Nevertheless, I think there's useful information in my original answer, so I'm leaving it, with updates below.
Round 1: Why An Aquatic Mammal Won't Develop an Eel-Like Dorsal Fin
An aquatic reptile certainly could (and indeed Marine Iguanas are already part way there), but an aquatic mammal probably wouldn't. As evidenced by the fact that they haven't.
Having enough vertebrae isn't the issue. A mammal could certainly develop a continuous, eel-like dorsal fin if it served some purpose other than providing propulsion for swimming. Structurally, it's no problem. But mammal spines and those of fish, amphibians, and reptiles work differently. Mammal spines (and those of birds) are designed to flex up-and-down (or front-to-back), which is very useful for efficient walking and running with vertically-oriented limbs held under the body. Fish and reptile spines, on the other hand, are designed to flex side-to-side. As far as the fish are concerned, as far as I know, that's just how it happened, just because; either orientation would've been fine, as evidenced by the fact that aquatic mammals can swim just fine. But reptiles and amphibians have kept that spine orientation because it works just fine when your limbs are splayed out to the side.
That's why aquatic mammals tend to develop horizontal fins and flukes for propulsion, and only relatively tiny dorsal fins for stability. It's much easier to do that, taking advantage of the direction of which the spine already naturally flexes to produce the most power, than it is to re-evolve a side-to-side flexing spine first. So if you want an aquatic mammal that uses an eel-like fin for propulsion, you'll first have to figure out what evolutionary pressures caused its ancestor to redevelop the appropriate spinal structure.
Round 2: Anguilliform Swimming With Horizontal Fins and a Mammalian Spine
Mammals certainly have enough vertebrae to make this sort of swimming possible. I'm not sure I know of any mammals which actually exhibit precisely that motion, but if you look at, e.g., otters, while they primarily use their limbs for propulsion, they are certainly capable of waving their bodies. They're probably better adapted to sub-carangiform locomotion, but it wouldn't take much to extend their flexibility to true anguilliform swimming.
As far as anchoring the fins, though... I don't really see a good way to do that. Rigid supports are not particularly necessary, but it is hard to see what sort of evolutionary pressures would lead to the development of a fin extending from the side of the body wall, whether entirely fleshy or not. If an aquatic mammal were to adopt this mode of swimming for some reason, it would seem more likely that the torso would simply widen and flatten out, with little or no distinct fin.
There are, however, mammals which already do have fin-like structures extending from the sides of the body walls: bats, flying squirrels, and the like. I could quite easily see, e.g., a diving bat developing into a full-time aquatic creature and adapting its wings into fins, anchored to and supported by the limbs and fingers. My primary expectation would be for such a creature to develop more rajiform propulsion, with undulations mainly restricted to the fin surface (in which case flexibility of the spin becomes largely a non-issue); however, I could imagine something like an aquatic flying squirrel, which has less of a well-developed wing surface and more just flaps of skin running along and projecting out from the body wall and lacking fine control, developing spine-driven anguilliform swimming, with the front limbs eventually reducing to little more than structural support for the leading fin surface, and the back limbs possibly disappearing entirely (as they did in dolphins and whales).