Naming conventions for digital files can be as easy or as complicated as you like. Either way, it's not something you should overlook. It makes an incredible difference when you or someone else is looking for a specific photo or groups of photos to have things well organized.
So what's the best way? My preference is to keep it simple.
Last name, first name subject YYYYMMDD.xxx
Jones, Sally birthday 1956-03-26.jgp
Jones, Peter draft card 1917.tiff
This works for me because I like to be able to sort by person or subject. If your collection or personal preference warrants it, put the date first so you can sort by date.
Some scanners give you the option of selecting the name of your file as you begin your scanning and will automatically apply that name plus a number to each new file. So your trip to Greece in 1995 can be scanned as "Jones Family Greece trip 1995 1.jpg" without having to rename every file. Be sure to check if your scanner has this function!
Personally, I don't need more information for my files. If you enjoy using the various scan settings to alter your original photos, or if you have printing needs that require attention to the resolution of the image, you may want that in your file name as well. You can read a very good article about this here.
Just remember... don't make yourself crazy trying to come up with a perfect naming convention. Scanning photos is a big undertaking and the important thing for future generations is to make sure those pictures are scanned and saved in a safe place.