diff --git a/lxc_net/container.py b/lxc_net/container.py
index 49951f0..4a7adcd 100644
--- a/lxc_net/container.py
+++ b/lxc_net/container.py
@@ -12,11 +12,11 @@ import weakref
 
 
 class OverlayDirectory:
-    """ Allocates an overlayfs with a given lower dir and a temporary upper dir. The
-    overlayfs is destroyed when this object is deallocated """
+    """Allocates an overlayfs with a given lower dir and a temporary upper dir. The
+    overlayfs is destroyed when this object is deallocated"""
 
     class DoesNotExist(Exception):
-        """ Raised if `lower` does not exist """
+        """Raised if `lower` does not exist"""
 
         def __init__(self, path):
             self.path = path
@@ -38,7 +38,8 @@ class OverlayDirectory:
             root_temp_dir.mkdir()
 
         self.overlay_temp_dir = tempfile.TemporaryDirectory(
-            prefix=name + ("_" if name else ""), dir=root_temp_dir.resolve(),
+            prefix=name + ("_" if name else ""),
+            dir=root_temp_dir.resolve(),
         )
         self.temp_dir = Path(self.overlay_temp_dir.name)
         self.temp_dir_cleaner = None
@@ -95,7 +96,7 @@ class OverlayDirectory:
         self.mounted = False
 
     def _set_perms_for_cleanup(self):
-        """ Sets the permissions to allow cleanup """
+        """Sets the permissions to allow cleanup"""
 
         if not self.temp_dir.exists():
             return  # Already deleted
@@ -131,7 +132,7 @@ class Container(util.LibvirtObject):
             return "This container is already instanciated"
 
     def __init__(self, conn, networks, name=None, mem=int(1e6), enable_v4=True):
-        """ Parameters:
+        """Parameters:
         * conn: connection to libvirt,
         * networks: iterable of Network instances this container is connected to,
         * name: name of the container. Defaults to something id-based.
@@ -142,9 +143,9 @@ class Container(util.LibvirtObject):
 
         super().__init__(conn)
 
-        if not name:
-            name = str(self.id)
-        self.name = settings.PREFIX + "_dom_" + name
+        self.name = f"{settings.PREFIX}_dom{self.id:02d}"
+        if name:
+            self.name += "_" + name
 
         self.networks = networks
         self.mem = mem
@@ -159,14 +160,14 @@ class Container(util.LibvirtObject):
         return self.lxc_container is not None
 
     def get_jinja_networks(self):
-        """ Get a jinja2 environment-compatible network list """
+        """Get a jinja2 environment-compatible network list"""
         return [
             {"mac": util.MACAddress(net.id, self.id), "name": net.name, "net": net}
             for net in self.networks
         ]
 
     def _create_network_files(self):
-        """ Creates systemd-networkd .network files to set IP addresses """
+        """Creates systemd-networkd .network files to set IP addresses"""
         if not self.overlay_root:
             raise Exception("No root directory specified yet")
         net_config_templ = JinjaTemplate("nic.network")
@@ -204,8 +205,8 @@ class Container(util.LibvirtObject):
         self.lxc_container = self.conn.createXML(xml)
 
     def notify_cleanup(self):
-        """ This method can be called before `cleanup` to notify the host that a
-        cleanup will be performed soon, speeding the process up. """
+        """This method can be called before `cleanup` to notify the host that a
+        cleanup will be performed soon, speeding the process up."""
         if self.lxc_container:
             try:
                 self.lxc_container.shutdown()