Ab Stretch gibt es Standard mässig kein eth* mehr.
Hier ein recht interessanter Link dazu:

Will man nun wenn man ein laufendes System hat was man ständig updatet eth0 behalten bedarf es einer udev Änderung und einen Kernel Parameter.

Ansonsten wird aus eth0 bei einem reboot plötzlich sowas wie enp0s3. Was dann einen ordentlichen Aufwand mit sich bringt wenn man in allen Programmen eth* ändern muss.

Um es kurz zu machen. Auf einem laufendem System machen wir nun folgendes um eth0 zu behalten.
Die Hintergrund Informationen dazu stehen in der unten angefügten Readme von udev.

In der Datei: /etc/default/grub fügen wir in der Zeile GRUB_CMDLINE_LINUX_DEFAULT folgendes ein: net.ifnames=0

Danach noch folgenden Befehl ausführen:

ln -s /dev/null /etc/udev/rules.d/80-net-setup-link.rules

Soltet Ihr noch eine /etc/udev/rules.d/70-persistent-net.rules auf eurem System haben muss diese gelöscht werden.

Abschließend initramfs und grub auf den neusten Stand bringen:

update-initramfs -u

Hier die entsprechende Readme dazu:

This documents udev integration Debian specifics. Please see man udev(7) and
its referenced manpages for general documentation.

Network interface naming

Since version 197 udev has a builtin persistent name generator which checks
firmware/BIOS provided index numbers or slot names (similar to biosdevname),
falls back to slot names (PCI numbers, etc., in the spirit of
/dev/disks/by-path/), and then optionally falls back to MAC address, and
generates names based on these properties. This provides "location oriented"
names for PCI cards such as "enp0s1" for ethernet, or wlp1s0" for a WIFI card
so that replacing a broken network card does not change the name. As location
based naming does not work well for USB devices, these use a MAC based naming
schema (see /lib/systemd/network/01-mac-for-usb.link).

This has been enabled by default since udev 220-7, which affects new
installations/hardware. Existing installations/hardware which already got
covered by the old 75-persistent-net-generator.rules will keep their interface
names, see below.

You can disable these stable names and go back to the kernel-provided ones
(which don't have a stable order) in one of two ways:

  - Put "net.ifnames=0" into the kernel command line (e. g. in
    /etc/default/grub's GRUB_CMDLINE_LINUX_DEFAULT, then run "update-grub").

  - Disable the default *.link rules with
    "ln -s /dev/null /etc/udev/rules.d/80-net-setup-link.rules"
    and rebuild the initrd with "update-initramfs -u".

See this page for more information:

Legacy persistent network interface naming

Debian releases up to 8 ("Jessie") and Ubuntu up to 15.04 had an udev rule
/lib/udev/rules.d/75-persistent-net-generator.rules which fixed the name of a
network interface that it got when its MAC address first appeared in a
dynamically created /etc/udev/rules.d/70-persistent-net.rules file.

This had inherent race conditions (which sometimes caused collisions and
interface names like "rename1"), required having to write state into /etc
(which isn't possible for read-only root), and did not work in virtualized

This old schema is deprecated in Debian 9 ("Stretch"), and will not
be supported any more in Debian 10.

Migration to the current network interface naming

On package upgrade systems will keep their current names, but they will need to
be manually migrated by Debian 10 / Ubuntu 18.04 LTS.  If you rely on the old
names in custom ifupdown stanzas, firewall scripts or other networking
configuration, these need to be updated to the new names.

First, determine all relevant network interface names: those in
/etc/udev/rules.d/70-persistent-net.rules, or if that does not exist (in
virtual machines), in "ip link" or /sys/class/net/.

Then for every interface name use a command like

  grep -r eth0 /etc

to find out where it is being used.

Then on "real hardware" machines, rename the file to
70-persistent-net.rules.old; on VMs remove the file
/etc/udev/rules.d/80-net-setup-link.rules instead.

Reboot, adjust configuration files, and test your system.

Custom net interface naming

In some cases it is convenient to define your own specific names for network
interfaces. These can be customized in two different ways:

 * You can create your own names via udev rules, based on arbitrary attribute
   and property matches. See man udev(7) for documentation how to write udev
   rules. For example, you can create /etc/udev/rules.d/76-netnames.rules with

   ------------ snip ----------
   \# identify device by MAC address
   SUBSYSTEM=="net", ACTION=="add", ATTR{address}=="11:22:aa:bb:cc:33", NAME="eth-dmz"

   \# identify by vendor/model ID
   SUBSYSTEM=="net", ACTION=="add", ENV{ID_VENDOR_ID}=="0x8086", \
       ENV{ID_MODEL_ID}=="0x1502", NAME="eth-intel-gb"

   \# USB device by path
   \# get ID_PATH if not present yet
   ENV{ID_PATH}=="", IMPORT{builtin}="path_id"
   SUBSYSTEM=="net", ACTION=="add", ENV{ID_PATH}=="*-usb-0:3:1*", NAME="eth-blue-hub"
   ------------ snip ----------

   The name of the rules file needs to have a prefix smaller than "80" so that
   it runs before /lib/udev/rules.d/80-net-setup-link.rules, and should have a
   prefix bigger than "75" so that it runs after 75-net-description.rules and
   thus you can use matches on ID_VENDOR and similar properties.

 * Unless you disabled net.ifnames, you can change the policy
   (kernel/bios/path/MAC based naming) in an /etc/systemd/network/*.link file,
   for individual devices or entire device classes. See man systemd.link(5) for
   details about this. /lib/systemd/network/99-default.link is the default
   policy, and /lib/systemd/network/01-mac-for-usb.link makes it use MAC based
   names for USB devices.

Any of the above changes require an initrd update with "update-initramfs -u" to
get effective.