Use prop_search(), a StringProperty and a CollectionProperty.

import bpy

enum_items = (
    ('FOO', 'Foo', ''),
    ('BAR', 'Bar', '')
)

class HelloWorldPanel(bpy.types.Panel):
    """Creates a Panel in the Object properties window"""
    bl_label = "Hello World Panel"
    bl_idname = "OBJECT_PT_hello"
    bl_space_type = 'PROPERTIES'
    bl_region_type = 'WINDOW'
    bl_context = "object"

    def draw(self, context):
        layout = self.layout

        obj = context.object

        col = layout.column()        
        col.prop_search(context.scene, "coll_string", context.scene, "coll", icon='OBJECT_DATA')

def populate_coll(scene):
    bpy.app.handlers.scene_update_pre.remove(populate_coll)
    scene.coll.clear()
    for identifier, name, description in enum_items:
        scene.coll.add().name = name

def register():
    bpy.utils.register_module(__name__)
    
    bpy.types.Scene.coll = bpy.props.CollectionProperty(
        type=bpy.types.PropertyGroup
    )
    
    bpy.types.Scene.coll_string = bpy.props.StringProperty()
    
    # Hack for testing
    bpy.app.handlers.scene_update_pre.append(populate_coll)


def unregister():
    bpy.utils.unregister_module(__name__)
    del bpy.types.Scene.coll
    del bpy.types.Scene.coll_string


if __name__ == "__main__":
    register()

For limitations please read:
Is it possible to use bpy.props.PointerProperty to store a pointer to an object?

Use prop_search(), a StringProperty and a CollectionProperty.

import bpy

enum_items = (
    ('FOO', 'Foo', ''),
    ('BAR', 'Bar', '')
)

class HelloWorldPanel(bpy.types.Panel):
    """Creates a Panel in the Object properties window"""
    bl_label = "Hello World Panel"
    bl_idname = "OBJECT_PT_hello"
    bl_space_type = 'PROPERTIES'
    bl_region_type = 'WINDOW'
    bl_context = "object"

    def draw(self, context):
        layout = self.layout

        obj = context.object

        col = layout.column()        
        col.prop_search(context.scene, "coll_string", context.scene, "coll", icon='OBJECT_DATA')

def populate_coll(scene):
    bpy.app.handlers.scene_update_pre.remove(populate_coll)
    scene.coll.clear()
    for identifier, name, description in enum_items:
        scene.coll.add().name = name

def register():
    bpy.utils.register_module(__name__)
    
    bpy.types.Scene.coll = bpy.props.CollectionProperty(
        type=bpy.types.PropertyGroup
    )
    
    bpy.types.Scene.coll_string = bpy.props.StringProperty()
    
    # Hack for testing
    bpy.app.handlers.scene_update_pre.append(populate_coll)


def unregister():
    bpy.utils.unregister_module(__name__)
    del bpy.types.Scene.coll
    del bpy.types.Scene.coll_string


if __name__ == "__main__":
    register()

For limitations please read:
Is it possible to use bpy.props.PointerProperty to store a pointer to an object?