This is right actually. The bone must also have the “deform” property checked, which helps the skinning process by excluding controllers, etc. from undesired vertex assignments
Ok can you have a look at my file and write out step by step what needs to be done (missing nothing at all). Because naming the bone and the vertex group the same doesn’t work on this file.
Group “L_Hnd_Th” is correctly assigned to the corresponding bone.
You can see it:
in Edit Mode by enabling vertex weight overlay with Viewport Overlays > Shading > Vertex Group Overlays (and selecting a group in Vertex Groups)
or in Weight Paint Mode by selecting Armature and Object. You can select (and pose) bones/groups by holding down Ctrl and clicking on a bone. If it’s purple - no group is assigned to the bone.
Btw, Armature is not actually deforming anything, because Object is not yet parented to it (and doesn’t have the Armature Modifier).
Simply select Object, then Armature and press Ctrl + P > Armature Deform