...I won't find it easy to find the others then...
Just search your PC for "*.sdltb" and move everything to your new location. From then on, all your termbases will be in the new location.
...I'll have to write a name or part of it which means I will have to remember the file's name.
You will find them all in your new location. It is always a good idea to name your termbases consistently and include basic data like customer, languages, field, etc. However, if for some reason you misplaced a file, you can always search your PC for "*.sdltm" to find all termbases in your drives.
Will I still be able to fins everything in Studio if I move them or copy/paste them in another folder?
Yes, in the open dialogue, navigate to your new location to open/import/use your termbases.
...by the way, it's really annoying having to move everything at the end of a day.
You don't have to do this. When you use a termbase from your new location, it will be saved/updated there. When you create a new termbase, just remember to create it in your new location. There is a specific field for this in the create new termbase dialogue.
Hope this helps.