One possible solution is to batch rename all your video files to match the creation date. There are a lot of free applications that can batch rename files for you. If you don't want to change the original file names of your clips, you should first make a copy of the files.
Every file name will need to be different, if you have a more than one clip recorded on the same day you will need to add a incrementing number of some other value to avoid duplicates.
Here I have used Advanced Renamer to rename the files based on the meta data:
Import your footage into Premiere, arrange the clips how you like and add the 'Clip Name' effect from the Effects panel to one of your clips. An overlay on the video will display the file name.
If you want to hide the incrementing number and file extension at the end of the file name, you can either position the text far enough right that it is out of frame or use a rectangular mask to hide it.
Once you have adjusted the text in the way you like, copy the clip, select all the other clips in your sequence and use 'Paste Attributes' under the right-click menu to add the effect.