Not all models have names. This style of case. Movement sits in a cup in the case back
depending on size. Maybe a 23.x or 26.5 caliber. You would need to remove the movement from the back and check under the balance wheel by the edge. If you’re not sure. Find a watch maker to do it and take some pictures
that lume is likely to be radium, probably best to avoid having any contact with it. Put it in a an appropriate container and let a professional sort it out for you, if that's what you decide to do.