How to increase the number of SQL Server Error Log files

To increase the number of SQL Server Error Logs, in SQL Server Management Studio Object Explorer:

Expand "Management" -> Right click on "SQL Server Logs" -> click "Configure":

sql server logs configure

In "Configure SQL Server Error Logs" window choose a value for "Maximum number of error log files" and click OK:

sql server maximum log files

To see how to cycle SQL Server Error Log files using DBCC ERRORLOG, read related blog post:
Cycle SQL Server Error Log files using DBCC ERRORLOG