I found that a journal changed its name after 2005. The paper which I am citing is from 2004. Does it matter if I use the current journal name or should I cite the paper using the (old) journal name in 2004?
Cite the journal name that was used at the time of publication. For example, the British Medical Journal officially changed title to BMJ in 1988. Cite articles from 1987 and earlier as Br Med J, not BMJ.