Do you connect an application to the load balancer name or the cluster name?
Let's assume this is just a Windows Server Failover Cluster and that there is no Always On availability group involved. 

The terms are often used somewhat interchangeably, so I don't know what your DBA or server admin calls them. But in the Failover Cluster management console, there are the following terms and concepts.


Cluster Name. This is the name for the Windows Server Failover Cluster, and is independent of any resources (SQL in your case, but other resources (DHCP, file server, generic services) can be added to a cluster). This is not what you want to point any SQL-using application to.
Node Name. This is the name of each server in the cluster. This would be used if you want to connect to a specific member of the cluster, without regard to whether the clustered service (i.e., SQL) is running on that node or on another one. Generally used for OS management tasks, this is also not what you want to point your SQL-using application to.
Server Name. This is where it really gets confusing. Within each role of a cluster (SQL Server in your case), there is a resource line item called "Server Name". That's the name (and associated IP address) that the role listens to. That name/address is the one that swings back and forth between the nodes whenever there is a failover. This is the one that you want to point your SQL-using applications to. (The IP address associated with this Server Name, and sometimes the name itself, is often called a "Virtual IP Address" or "VIP", referring to the idea that the IP address doesn't belong to a specific server.)


I suspect that the person providing this information to you is using "load balancer" to refer to the Server Name that you should point your application to. The term "load balancer" is a bit mis-used in this case, because there isn't really any balancing happening -- either by round-robin or by resource capacity.