ntoe on Flickr, IMGUR, Smugmug - they all work great, and work going forward as you go. But they all replace the filenames on your uploaded images. If you have a lot of previous images you are looking to go replace in old topics, it's going to be a gigantic pain in the rear try to match things up. Depending on how many old images you have to replace. I've got at least 1500++ across several years and forums.
I have not yet been able to find a service that will retain my file names. And am now casting about for some online storage space where I can upload that library of images and link to them. Might even wind up with my own domain and website hosting plan to do it.
A little hacky, but have you considered putting the filename in the title or caption prior to uploading to a new system? If you put it there I know Flickr will automatically read it and put it in the Title or Description fields. That would at least allow you find the appropriate file for replacing the Photobucket embed.
A quick and easy way to do this would be with exiftool. Works on
Mac, PC
or
Linux. A simple command line tool it's incredibly powerful. To put the filename in the IPTC Caption field simply use this:
exiftool "-iptc:caption-abstract<filename" [path/to/file]
Obviously replace [path/to/file] with the actual path to the file.
If you want to do a whole directory or series of directories use:
-r [path/to/directory] instead of [path/to/file]