Availability groups multiple instance, multiple listeners In my work environment, I have two database machines:

DB01
DB02

Each database machine has three SQL Server instances:

MSSQLSERVER
FBG
Central

I've managed to set up availability groups with SQL Server listener for the 1st SQL Server instance on both machines, and created SQL Server replication and it's working fine.
Now, I would like to set up a new availability group for the second SQL Server instance FBG on both servers, and I did, but the problem is when I create the listener for the second availability group it goes for the first availability group, I must type listener name / instance name to get it working.
I wish to type only the availability group listener name. For example:

the first availability group name is AVG01 and its listener AvgList01
the second availability group name is AVG02 and its listener AvgList02

When I connect to AVG02 using the name AvgList02 it connects me to AVG01
although I'm not using its listener name.
I must use it this way to get it working AvgList02\FBG where the FBG is the name of the SQL Server instance.
The question
Where is the issue, and how to fix it?
When I connect to AVG02 using the name AvgList02 it connects me to AVG01 although I'm not using its listener name. Where is the issue, and how to fix it?  


Consider port configuration play key role in general. In your case most probably following might happened.


Both availability groups's primary replica is same node (DB01 or DB02)
There must be SQL Browser service running in each SQL Server
Default SQL ports (1433) must have been assigned for listeners


When client tries to connect on listener name the IP would be bounded based on DNS response (in multi sub-net first successful IP bound) which lead client connection to pointing to primary replica.

Connection from AvgList02 to AG01 (AVG01):
When the request hitting primary replica (after IP bound from listener name), next part is port (consider wrong port as per point 3) the connection would be established to the service which is running on particular port number (1433). 

Connection from AvgList02\FBG to AG02 (AVG02):
Similar to above case (after IP bound from listener name), since the instance name (FBG) mentioned in connection SQL Browser would take action to bound the connection with respective SQL Service that match with instance name mentioned in connection.

Summary:
I personally recommend to use custom port for SQL Server especially when multiple instances running in same server, and disable SQL Browser service, let every connection hard-code custom port number in connection string to connect respective instance without depending on SQL Browser service. 

For availability group implementation, consider custom ports and avoid port conflict in following sections:


SQL ports (Default: 1433)
Endpoint ports (Default: 5022)
Listener ports (no default)