Set the primary DNS suffix on Windows

Right Click PC -> "Properties" -> "Computer Name" -> "Change..."

will typically get the DNS suffix from the DHCP server.

Append primary and connection specific DNS suffixes

specifies that resolution for unqualified names that are used on this computer are limited to the domain suffixes of the primary suffix and all connection-specific suffixes. Connection-specific suffixes are configured in DNS suffix for this connection.

The primary DNS suffix is configured by clicking Properties on the Computer Name tab (available in System in Control Panel). The local setting is used only if the associated Group Policy is disabled or unspecified.

For example, if your primary DNS suffix is dev.wcoast.microsoft.com and you type ping xyz at a command prompt, the computer queries for xyz.dev.wcoast.microsoft.com. If you also configure a connection-specific domain name on one of your connections for bldg23.dev.wcoast.microsoft.com, the computer queries for xyz.dev.wcoast.microsoft.com and xyz.bldg23.dev.wcoast.microsoft.com.

Connection-specific DNS Suffix

To complete unqualified domain name system (DNS) names that will be used to search and submit DNS queries at the client for resolution, you must have a list of DSN suffixes that can be appended to these DNS names. For DHCP clients, this can be set by assigning the DNS domain name option (Option 15) and providing a single DNS suffix for the client to append and use in searches.

In some circumstances it is preferable that a DHCP client be configured by using multiple DNS suffixes, supported with the use of DHCP Search Option 119.

DHCP Search Option 119 is passed from the DHCP server to the DHCP client to specify the domain search list used when resolving hostnames with DNS. DHCP Search Option 119 applies only to DNS and does not apply to other name resolution mechanisms.

DNS domain suffix

So I'm not fully understanding how it can intermittently appear or not appear, unless the machine is not configured wtih a Primary DNS Suffix, because the Primary DNS Suffix is automatically the defeault Search Suffix. Option 015 allows you to add search suffixes only for the interface that is getting a DHCP address. So if you have a machine joined to the domain, that automatically has the suffix. If a non-joined machine connects, it won't have one unless 015 is configured, but for the options to come across, a DHCP Relay Agent must be used.

More from my notes on this:(Windows)

By default, DHCP Options are NOT passed to a RRAS client (dialup or VPN). Instead, this information is taken directly from the RAS server's NIC settings, and may not be the DNS or WINS server addresses you want to give the VPN clients. If a RAS server has WINS or DNS entries, these entries are passed to the client.

DHCP Option

015           # Specifies the connection-specific DNS domain suffix to be used by the DHCP client.

119           # DNS Domain Search List option to specify the domain search list used when resolving hostnames with DNS.

Register this connection's addresses in DNS

specifies that the computer attempt dynamic registration of the IP addresses (through DNS) of this connection with the full computer name of this computer, as specified on the Computer Name tab (available in System in Control Panel)

Juniper

# Code     opt_name        opt_value

119        domain-search   Domain Name

Windows 7 does not request DHCP option 119

You'll have to look at other options, eg pushing out a search list via GPO etc.

15  domain-name String

This option specifies the domain name that client should use when resolving hostnames via DNS.

Query

Win10

Windows 10 changed the way DNS works.
Now DNS queries are sent to all DNS servers simultaneously.
The first to respond is taken as the "winner".

In your case, Google might respond a millisecond faster and that's all it takes.
Google won't know about your internal domain name so that "no such hostname" failure is cached for a while.
Until the TTL is reached and it will try again.
The next time, the DC might respond a fraction of a second faster.

Do not mix public and private DNS.
If you have an internal-only domain such as Active Directory, only use internal DNS servers.