There is no limit to variable name size in the Java Language Specification. However, there is an implicit implementation limit in the class file format (The Java Virtual Machine Specification):
The length of field and method names, field and method descriptors, and other constant string values (including those referenced by ConstantValue (§4.7.2) attributes) is limited to 65535 characters by the 16-bit unsigned length item of the CONSTANT_Utf8_info structure (§4.4.7).