For expanding out Java classes I want to get the currently-being-edited file's base name.
Try to use snip.basename in a python interpolation.
As an example, write this snippet in your java.snippets file:
snippet foo ""
`!p snip.rv = snip.basename`
endsnippet
Insert foo in your .java file and press the key to expand the snippet; the result should be the basename of the current file.

For more information, see :h Ultisnips-python.
If you have other usage questions, try to visit https://vi.stackexchange.com/ and tag your question with plugin-ultisnips.
Most helpful comment
Try to use
snip.basenamein a python interpolation.As an example, write this snippet in your
java.snippetsfile:Insert
fooin your.javafile and press the key to expand the snippet; the result should be the basename of the current file.For more information, see
:h Ultisnips-python.If you have other usage questions, try to visit https://vi.stackexchange.com/ and tag your question with plugin-ultisnips.