When we search the name of website without www. or extension like .com or any other then if website appears in search then its not penalized nor banned and if we don’t find it then it may be penalized or banned.
Yes. There are 2 ways to check the penalized or banned websites.
1. Through Google Webmaster tool, check the status of your website.
2. Manually check by typing the name or url of your website on search box. If its not there, it means your website's got penalized or banned.
There are many ways to check penalized or banned websites
1) Check If You’ve Received Warning Message in Google Webmaster Tools
2) Check What Day Did Your Traffic Drop
3) Check If You Lose Organic Rankings of Your Target Keywords
4) Ask Your SEO Company (If You Have One)
Through Google Sandbox and Penalty Checker Tool, you can check your website and also you have focus on few things such as:
Check If You’ve Received Warning Message in Google Webmaster Tools.
Check What Day Did Your Traffic Drop.
Check If You Lose Organic Rankings of Your Target Keywords.