Changing the file extension can cause file corruption?

I have some video which I thought was an MP4 file. But it shows no extension and when I opened it, my computer asked me to which program I will open the file. So I decided to add a.mp4 file extension into it and the ison changed to default program from where it will be use. Is it safe to rename or modify the file extension of a specific file? Will it damage or corrupt the file?
