Could Java somehow identify me? Should I uninstall Java from my computer if I want to use the Tor browser anonymously?
As @Steve mentioned in the comment, Tor Browser does not use Java nor does it support Java applets. So, there's no need for it to interact with your local Java installation. (Try executing any Java applet -- it will fail.)
However, the Tor Browser Bundle is a sandbox. TBB tries to only use the files and data that it has in its installation directory and does not touch other applications on your system, except for the operating system itself.
It's also safe to run e.g. Java applications while you use TBB. Your host operating system is responsible for securing the memory etc., so that there are no lacks compromising your system security.
Another aspect is the Java application that you execute locally. If it's a "bad" application that sends your real IP to its servers and manages to e.g. connect to Tor Control Port (or at least detect a runnig Tor process), you may be not anonymous anymore. This is true for almost all software.
(If the hacker makes you run his software on your computer, it's not your computer anymore.)