While migrating from Tomcat to Weblogic 12.1.3 I got this exception
javax.naming.namenotfoundexception while trying to look up
ds = (DataSource) initContext.lookup("MyDB");
Unlike Tomcat, weblogic creates multiple servers (Usually an Admin Server, plus at least one other). Each server has to be allocated the data source. In a clustered environment, you need to apply the datasource to the cluster servers.
You should be to connect to the datasource as normal. I always use a Spring JNDI bean, so I can't help with the exact syntax. The suggestions by @Maas look good.