The answer is 100% correct but I will add a little to it as it totally confused me when I first used Linux.
"I do not want to move the file, I just want to rename it" was myMSDOS thought process. Well the mv command does both at the same time.
The following variations may help.
mv /oldlocation/oldname /oldlocation/newname
mv /oldlocation/oldname /newlocation/newname
mv /oldlocation/oldname /newlocation/oldname
Sorry if this is stating the obvious