Configuring Cisco DNS ?

Question

Domain Name System

There is a Cisco 7200, you need to configure it so that site.com gives out my DNS server, or my DNS is used for all sites. But the first option is better. Thank you!
I understand that you need to register anywhere

ip domain lookup
ip name-server 127.0.0.1 8.8.4.4
ip domain name site.com
ip dns server

Instead of 127.0.0.1 is the DNS address, instead of site.com is the site address. But this option does not work.

!* 7200L.CiscoConfig
!* IP Address : 111111111111111
!* Community  : private
!* Downloaded 10/29/2014 10:55:56 AM by SolarWinds Config Transfer Engine Version 5.5.0

!
version 12.2
service nagle
no service pad
service tcp-keepalives-in
service tcp-keepalives-out
service timestamps debug datetime msec localtime show-timezone
service timestamps log datetime msec localtime show-timezone
service password-encryption
!
hostname 7200L
!
boot system flash slot0:c7200-is-mz.122-19a.bin
boot bootldr bootflash:c7200-boot-mz.120-22.S.bin
logging buffered 128000 debugging
logging console informational
enable secret 5 $1$fUeS$CLcGl0RQmntGEpjAfb28e1
!
username admin password 7 111111111111111111111
clock timezone est -5
ip subnet-zero
no ip source-route
ip cef
!
!
no ip domain-lookup
ip dhcp excluded-address 69.27.242.65
ip dhcp excluded-address 69.27.242.66
ip dhcp excluded-address 69.27.242.67
ip dhcp excluded-address 69.27.242.68
ip dhcp excluded-address 69.27.242.69
ip dhcp excluded-address 69.27.242.70
ip dhcp excluded-address 69.27.242.71
!
ip dhcp pool lab
   network 69.27.242.64 255.255.255.224
   dns-server 4.2.2.6 4.2.2.5 
   default-router 69.27.242.65 
   domain-name labservices.com
   lease 0 0 30
!
no ip bootp server
ip multicast-routing
call rsvp-sync
!
!
!
!
!
!
controller T1 2/0
 framing esf
 linecode b8zs
 channel-group 0 timeslots 1-24
 description 866-611-3434 01DHXS100414
!
controller T1 2/1
 framing esf
 linecode b8zs
!
controller T1 2/2
 framing esf
 linecode b8zs
!
controller T1 2/3
 framing esf
 linecode b8zs
!
!
policy-map SETDSCP
policy-map Traffic
!
!
!
interface FastEthernet0/0
 description DMZ Int
 ip address 69.27.242.65 255.255.255.224
 ip helper-address 172.17.6.99
 no ip redirects
 no ip unreachables
 no ip proxy-arp
 ip accounting output-packets
 ip accounting access-violations
 ip pim sparse-dense-mode
 no ip mroute-cache
 duplex full
 no cdp enable
!
interface Ethernet1/0
 no ip address
 no ip mroute-cache
 shutdown
 duplex full
 standby 13 ip 10.11.13.200
 standby 13 timers 1 3
 standby 13 priority 101
!
interface Ethernet1/1
 no ip address
 no ip mroute-cache
 shutdown
 duplex half
!
interface Ethernet1/2
 no ip address
 no ip mroute-cache
 shutdown
 duplex full
!
interface Ethernet1/3
 no ip address
 no ip mroute-cache
 shutdown
 duplex full
!
interface Serial2/0:0
 description 866-611-3434 01DHXS100414
 ip address 69.74.14.14 255.255.255.252
 no ip redirects
 no ip unreachables
 no ip proxy-arp
 ip accounting output-packets
 ip accounting access-violations
 ip pim sparse-dense-mode
 no cdp enable
!
ip classless
ip route 0.0.0.0 0.0.0.0 69.74.14.13
no ip http server
ip pim accept-rp auto-rp
!
logging trap debugging
logging facility syslog
access-list 2000 deny   ip host 69.27.242.70 any
access-list 2000 deny   udp host 69.27.242.70 any
access-list 2000 deny   icmp host 69.27.242.70 any
access-list 2000 permit ip any any
access-list 2000 permit udp any any
access-list 2000 permit icmp any any
dialer-list 1 protocol ip permit
no cdp run
snmp-server community msgprivlab RW
snmp-server community msglabnet RO
snmp-server community private RW
snmp-server community public RO
snmp-server packetsize 8192
snmp-server location OMP
snmp-server contact John Yacono
snmp-server enable traps tty
tacacs-server host 172.17.2.50
tacacs-server directed-request
tacacs-server key 7 11111111111111111111111
!
dial-peer cor custom
!
!
!
!
gatekeeper
 shutdown
!
!
line con 0
 password 7 111111111111111111111111111111111111111111111

end

Answer 1

you need to configure site.com to issue my DNS server, or for all sites to use my DNS

I didn't understand what you want to do. What does it mean "issued my DNS server"? Do you want a specific hostname to resolve to a given IP address? Then, in my opinion, you should:
1) activate the DNS server on 7200 (see document )
2) configure the DHCP server so that it distributes the necessary DNS settings
3) register the necessary name and address match ( ip host hostname ipaddress) on 7200
Or specify what you mean.
UPD :

Yes, you are completely right. Please show how to register this on the current config

If it is still relevant, then here is an approximate configuration. Before using it, I recommend saving the current configuration. I recommend testing the configuration during the period of least load.

ip dns server
ip name-server 8.8.8.8
ip dns server queue limit forwarder 10
ip host site.com 1.2.3.4
ip dhcp pool lab
 no dns-server 4.2.2.6 4.2.2.5 
 dns-server 69.27.242.65

In this case, it is assumed that the site.com domain must be resolved to 1.2.3.4 for all dhcp clients. In case you need to support your zone, the configuration will be different. After applying the configuration, I recommend observing resource consumption (show processes cpu, show processes memory).
I also hope to no longer observe harsh statements addressed to colleagues.