Hi 

we have a plan to deploy sharepoint 2013 internet portal and we are using sql server back end.

also we plan to make sql server cluster and always on

if we install a named sql server instance for sql server databases,

is it will be affect to sql server cluster and always on ?

 your question is unclear - but aliases to named instances should not cause any issue either sql cluster or always on but will add some confusion and make sure you have defined alias on each client.

always on does not require sql cluster - always on needs - windows cluster with stand alone sql instance (named/default)

sql cluster - windows cluster + clustered sql instance

If you have  the only SP databases dedicate to the server , I would consider two node SQL Server cluster environment