SQL Server connectivity without specifying tcp/port Having connection issues out of nowhere in my lab (Azure VMs):

SQL 2016, sp1, cu4 all the way around, Windows 2016 Datacenter

Windows Failover cluster for SQL AG testing.

SQLServer-0:

Default instance (port 1431)

Inst1 (port 1499)

SQLServer-1:

Default instance (port 1431)

Inst1 (port 1499)

From SQLServer-0, I can only connect to the remote instance(s) using tcp:SQLServer-1, 1431 (or tcp:SQlServer-1.kevinsdomain.com,1431).

Same thing for the named instance.

Same thing from SQLServer-1 to SQLServer-0.

Ping of just the NetBIOS name works just fine, ping -a resolves the FQDN.

None of these are running on port 1433, both servers are running SQL Browser under NT Authority\Local Service.

This is my test domain, along with a domain controller, DNS, etc.

Windows firewall on each has all of the ports open that are needed, including UDP 1434.

I'm sure there's something simple I've forgotten to check, flush, whatever.  Just can't think of it.
Just to clarify your question... you wish to connect to the instance on either server without the need to specify the Port Number? 

In that case, did you check if the instance name is added into your SQL configuration manager? 


Open SQL Configuration Manager
Expand "SQL Native Client Configuration"
Select "Aliases"
See that if the instance that you wish to connect exists, if no, create the alias for the instance


Hope I do answer your question...