Most journals require you to state your funding sources. I am a current phd candidate, submitting a paper as sole author, and my funding currently comes from a teaching assistantship, which is paid for by the department, not my advisor. I feel that people usually list any grants/awards in their funding acknowledgment. What am I supposed to put? "Supported by department X in X university?"
A TA doesn't directly fund your research. It funds you, personally and allows you to be a student. Your research hasn't been funded specifically other than the fact that you may have an office, etc. There is probably a tuition waiver, which is a sort of general funding.
You could list the department and university generally as you suggest. You could probably also list "none", but the department might be the better option.