Short of something "branded", you may have to trace the circuit to narrow down the identification.
In some cases, there was an audio amplifier stage that was sold seperate, kind of like the way Radiola juniors, and some Crosleys were sold. If it turns out that you have an amp, that is of value too.
There are some picture books on the early radios, but they are not always comlete, you can also look at what is on Ebay, and you can usually tell if the seller knows what they have- Often those that do give you a good image, and good description to use for ID.
:I found an old one tube radio in a wooden box (about 8 inch cube) with a lift top...the front looks like black phenolic and has two knobs. Its a battery set. Looks very old. Any ideas on how to identify it?