I added those options to the configuration:

default domain-name "lan";
default domain-search "lan";

What I get as a result:

domain lan
search lan.
nameserver 62.241.198.245
nameserver 62.241.198.246

There is an extraneous period that should not be there.

- -- System Information:
Debian Release: 11.0
  APT prefers stable-security
  APT policy: (500, 'stable-security'), (500, 'stable-debug'), (500, 'stable')
Architecture: amd64 (x86_64)

Kernel: Linux 5.10.0-8-amd64 (SMP w/8 CPU threads)
Locale: LANG=fi_FI.utf8, LC_CTYPE=fi_FI.utf8 (charmap=UTF-8), LANGUAGE=fi:en
Shell: /bin/sh linked to /bin/dash
Init: systemd (via /run/systemd/system)
LSM: AppArmor: enabled

Versions of packages isc-dhcp-client depends on:
ii  debianutils        4.11.2
ii  iproute2           5.10.0-4
ii  libc6              2.31-13
ii  libdns-export1110  1:9.11.19+dfsg-2.1
ii  libisc-export1105  1:9.11.19+dfsg-2.1

Versions of packages isc-dhcp-client recommends:
ii  isc-dhcp-common  4.4.1-2.3

Versions of packages isc-dhcp-client suggests:
pn  avahi-autoipd         <none>
pn  isc-dhcp-client-ddns  <none>
pn  resolvconf            <none>

- -- Configuration Files:
/etc/dhcp/dhclient.conf changed:
option rfc3442-classless-static-routes code 121 = array of unsigned integer 8;
send host-name = gethostname();
request subnet-mask, broadcast-address, time-offset, routers,
	domain-name, domain-name-servers, domain-search, host-name,
	dhcp6.name-servers, dhcp6.domain-search, dhcp6.fqdn, dhcp6.sntp-servers,
	netbios-name-servers, netbios-scope, interface-mtu,
	rfc3442-classless-static-routes, ntp-servers;
default domain-name "lan";
default domain-search "lan";


- -- no debconf information
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As additioal info. it seems that the additional period only appears if
dhclient is called for DHCP-IPv6 (stateful or stateless), such as in
the following /etc/network/interfaces stanza :

iface enp4s0 inet dhcp
iface enp4s0 inet6 auto
  privext 2
  dhcp 1

If the inet6 section is commented out, no extra period appears.

Martin-Éric

Still not fixed as of 4.4.3-P1-1.1:

domain internal
search internal. local.
nameserver 172.16.1.1
nameserver 1.1.1.1

Dear submitter,

as the package isc-dhcp has just been removed from the Debian archive
unstable we hereby close the associated bug reports.  We are sorry
that we couldn't deal with your issue properly.

For details on the removal, please see https://bugs.debian.org/1143544

The version of this package that was in Debian prior to this removal
can still be found using https://snapshot.debian.org/.

Please note that the changes have been done on the master archive and
will not propagate to any mirrors until the next dinstall run at the
earliest.

This message was generated automatically; if you believe that there is
a problem with it please contact the archive administrators by mailing
ftpmaster@ftp-master.debian.org.

Debian distribution maintenance software
pp.
Thorsten Alteholz (the ftpmaster behind the curtain)