Necturus beyeri likely consists of at least two distinct species (I would guess eastern and western populations), but these are all currently included in N.beyeri.
Necturus alabamensis is the concept you are probably dealing with. Formerly, this species was thought to have a fairly wide distribution across parts of four states, including most of Alabama. However, these were also found to be two species, with a striped form in the upper Black Warrior River being distinct from all the rest. THAT population owns the name N.alabamensis, which leaves all the rest without a name. Those are now refered to as N.cf.beyeri, which means "compare to N.beyeri". That means they're NOT beyeri, but are similar to them. All editions of the Peterson eastern field guide [so far] will identify N.cf.beyeri as N.alabamensis. True N.alabamensis has two pale dorsolateral stripes (juveniles), a plain white belly, and large dark blotches on the side, and it is flatter overall (similar to a mudpuppy). Salamanders of the United States and Canada [you DO own a copy of this don't you?] describes both forms in the section on N.alabamensis. Dick Bartlett's Guide and Reference to the Amphibians of Eastern and Central North America (North of Mexico) describes and illustrates all Necturus separately, including N.cf.beyeri.
N.beyeri has many small black spots on the belly and and larger spots on the dorsum. The body has a rounded shape. Juveniles are similar.
N.cf.beyeri has more and smaller dorsal spots than N.alabamensis, though the back can be so dark that the spots are hard to see. The belly is unmarked white. Juveniles are similar. The correct name for this species might be N.lodingi, though I doubt the original description for that name would apply.
N.punctatus has no dorsal spots or tiny black flecks. The underside is generally lighter than the brown dorsum and is unspotted. The head is flattened. Juveniles are similar.
I am of the opinion that no-one with an interest in North American herps, should be without a copy of at least one of the Peterson guides, and preferably both. That's a minimum. State/Province [in this case The Reptiles and Amphibians of Alabama; by RH Mount, while dated, is excellent for this subject] and taxon guides [Salamanders of the United States and Canada and Handbook of Salamanders] would be valuable additions to any library as well. These will be far more reliable than the sources often found more or less randomly online.