Nope, you can do it while it's on. The .vmx file will get updated accordingly. Now if you did this on the .vmx it woudl not register and after a powercycle, the old name would hold true.
you can rename it, but keep in mind that the folder on the VMFS volume, .vmx, .vmdk, and other files will retain the original name. This can get confusing when looking a datastores.