You'd have to use python for this. Make sure the collection that you'd like to render is selected/active in the Outliner and run the following script:
import bpy
import os.path
C = bpy.context
scn = C.scene
output_path = scn.render.filepath
exclude_type = ('LIGHT', 'CAMERA', 'ARMATURE', 'LIGHT_PROBE', 'SPEAKER')
Disable all relevant objects in renders
for ob in C.collection.objects:
if ob.type not in exclude_type:
ob.hide_render = True
for ob in C.collection.objects:
if ob.type not in exclude_type:
# Enable the object for rendering
ob.hide_render = False
# Assemble the path (.jpg is a placeholder)
scn.render.filepath = os.path.join(output_path, "{}.jpg".format(ob.name))
# Call the render operator
bpy.ops.render.render(write_still=True)
# Disable the object for rendering
ob.hide_render = True
Reset the output path
bpy.context.scene.render.filepath = output_path
Reset hide_render state
for ob in C.collection.objects:
if ob.type not in exclude_type:
ob.hide_render = False
Render output of the default scene, added a Sphere and a Cylinder to the default Collection:
/tmp/
├── Cube.png
├── Sphere.png
├── Cylinder.png
To get the shadow just add a Plane to the Scene Collection, make it a Shadow Catcher (Object Properties > Visibility) and enable Transparent (Render Properties > Film):

Render output of the shadow catcher scene (Cube.png, Cylinder.png, Sphere.png):

If you'd like to have a subfolder with the actual name of the collection, just add it to the regular output path e.g. /tmp/Collection/.
Related: