Use the utility in your script (depends on the shell or script you are using) and attach it to the filename.
When you are asking technical questions, you will get faster and better answers, and not waste others' time, by providing the details of what you are doing.
operating system? scripting language (bash, PHP, ksh, etc)? and other details.
If we have to reply back and forth many times, just to get basic info, it is a waste of both of our time.
If you convert to DMY format, will have have to write more code to instruct a computer to compare dates.
That's why UNIX time is so great.
You can easily compute with it.
On my backups, I use standard date and time format because I don't use the information to have a computer compare the dates / times.
So, I prefer human readable file names.
But if I was comparing the times using a computer, then I use UNIX time.
For example, when you logout of this forum, we set a cookie of your last login time, so when you login again, we know what posts you have not seen, based on time, etc.
Yes, because it will not overwrite the old backup.
That is a "good thing" because you don't want to automatically overwrite your backups.
The purpose of having backups is to have a lot of them incase there was a problem.
For example.
Let's say that in two weeks time, you discover a criminal hacked into your system a week ago and did some bad things.
If you only have the latest backup, two weeks from now, you will certainly not have the backup from three weeks ago (from two weeks in the future).
So, if you want to be safe and take care of your users and user data, you must have backups going back ... a long way... depending on how critical your data is.
Then, as a good sys admin, you delete your very old backups (manually is best) when you are confident you don't need them.
That's how it is done.
Otherwise, you will f*ed very much when you discover in a month someone hacked you two weeks ago from today