If you wish to audit logins successful/unsuccessful connections, once you enable audit you open View Audit Logs and can search for successful and unsuccessful login events. It should provide you useful information like hostname and IP address. Please click here for more details.
You can also audit successful/unsuccessful authentications and DML T-SQL statements for an specific database using PowerShell as shown below:
Set-AzureRmSqlDatabaseAuditing -ResourceGroupName "resourceGroup" -ServerName "SQL Server Name" -DatabaseName "AdventureWorksLT" -StorageAccountName "storageAccount" -AuditActionGroup "SUCCESSFUL_DATABASE_AUTHENTICATION_GROUP", "FAILED_DATABASE_AUTHENTICATION_GROUP", "BATCH_COMPLETED_GROUP" -AuditAction "UPDATE ON database::[AdventureWorksLT] BY [public]" -RetentionInDays 60
Another example, this time how to collect who dropped database objects on a specific database and schema:
Set-AzureRmSqlDatabaseAuditing `
-State Enabled `
-ResourceGroupName "resourcegroupname" `
-ServerName "ssqlinstancename" ` #ssqlinstancename.database.windows.net
-StorageAccountName "strageaccountname" `
-DatabaseName "dbname" `
-AuditActionGroup 'SCHEMA_OBJECT_CHANGE_GROUP' `
-RetentionInDays 8 `
-AuditAction "DELETE ON schema::dbo BY [public]"
Azure SQL Auditing should provide you the application name, duration, login name and client IP address that executed the query if you look for the event type BATCH_COMPLETED once you have enable Auditing. Please see above examples.
The Auditing feature won't screw up Log Analytics, Azure Monitor or Intelligence Performance features.