There are a couple of ways to have separate configuration files for each application:

1. You can place configuration files called log4j2<contextName>.xml on the classpath of all applications and configure a different <contextName> for each application. The default Log4j Core initialization process will find those files.
2. You can use the log4j2.configurationFile Log4j configuration property together with lookups so that the property evaluates to a different value for each web application.
3. You can use the log4jConfiguration Servlet initialization parameter recognized by the log4j-jakarta-web web fragment.

Setting the context name

The logger context name <contextName> is usually a hash of the web application classloader, so not really usable.
You can however change this in one of two ways:

1. You can add the log4j-jakarta-web artifact mentioned above to all your web applications. The artifact allows you to set <contextName> using the Servlet initialization parameter log4jContextName. If you don't set it up explicitly, it has some reasonable defaults (also documented in the log4jContextName description).
2. You can use a third-party context selector that sets up the context name based on the Tomcat component hierarchy: Tomcat Context Selector.

Of course my favorite approach is the one offered by the Copernik.eu extensions (I am the author).
There are a lot of subtleties, when dealing with logging in Tomcat (Tomcat JULI to Log4j API redirection, classloader delegation, etc.).
I created a Logging in Tomcat using Log4j Core Guide to deal with those altogether.

Using lookups in log4j2.configurationFile

In the log4j2.configurationFile you can use lookups, so for example you can add:

-Dlog4j2.configurationFile=${catalina.base}/conf/log4j2-${web:contextPathName}.xml

could work.