It would not be possible to automatically remove the preceding number and period before the filename in JuiceboxBuilder-Pro.
You'd need to go to 'Images -> Titles -> Use File Name' (or 'Images -> Captions -> Use File Name') and then manually edit each image title or caption (on the 'Images' tab).

It would be much easier to create the gallery (with the full filenames in use as the image titles or captions) and then edit the gallery's 'config.xml' file in a text editor which supports regular expression search and replace, like Notepad++. You could then remove the preceding number and period from all image titles and captions in a single search and replace action. You could even load up several 'config.xml' files and run the search and replace throughout multiple files at once.

If using Notepad++, here's what you could do.

(1) Open your gallery's 'config.xml' file(s).
(2) Go to 'Search -> Replace...' from the drop down menu at the top (Ctrl+H).
(3) Select 'Regular expression' as the 'Search Mode'.
(4) Enter CDATA\[[0-9]+\. in the 'Find what' input field.
(5) Enter CDATA[ in the 'Replace with' input field.
(6) Click the 'Replace All in All Opened Documents' button.

Including 'CDATA' in the search will handle both image titles and captions, ensuring that the imageURL and thumbURL entries are left unmodified.

Please note that using Notepad++ is just a suggestion (not a recommendation).
Notepad++ is free and I use it myself but other text editors are available.
However, if you use a different text editor, it may use a different regular expression engine and the syntax may differ from the search string in #4 above.

Also, be sure to make a backup of your gallery's 'config.xml' file before you edit it (just in case something goes wrong and you need to reinstate it at a later date).