Yes you can do "Contains" "Begins with" or "Ends with" for the naming convention.
ref (https://help.exacttarget.com/en/documentation/automation_studio/triggered_automations/)
When setting up a filename pattern, users select an operator to dictate how Automation Studio should parse the filename. The
available operators are Contains, Begins With, and Ends With.
Use Contains when Automation Studio should find files whose filename
includes the filename pattern at any point (prior to the file
extension, which is not parsed).
Example:
Filename pattern = AUG14
Files named AUG14import.csv, Update_ AUG14.txt, and
NewContactsAUG14profileupdates.zip will kick off this automation.
Files named AUG 14data.csv, CustomerFiles.AUG14, and
DailyJob-Aug-14.txt will not trigger this automation.
Use Begins With
when Automation Studio should find files whose filename starts with
the filename pattern.
Example:
Filename pattern = AUG14
Files named AUG14import.csv, aug14files.zip, and Aug14098786.txt will
trigger this automation. Files named 1AUG14data.csv, 120814_
AUG14.zip, and _ AUG14.txt will not trigger this automation.
Use Ends with when Automation Studio should find files whose filename ends with the filename pattern.
Example:
Filename pattern = AUG14
Files named ImportAUG14.csv, aug14_listpull_aug14.zip, and
usersAug14.txt will trigger this automation. Files named
datapullAUG14_01.csv, listinfoAUG14.run.txt, and Aug14_.zip will not
trigger this automation.
For the import activity, there are other personalization strings that can be used. https://help.exacttarget.com/en/documentation/automation_studio/triggered_automations/
Try using %%FILENAME_FROM_TRIGGER%% inside the import activity.
Substitution Strings
Place the following substitution strings in the "File Naming Pattern" field to call a file transfer activity or import activity. In other words, use these strings to import, upload, or download a file from a transfer location.
%%FILENAME_FROM_TRIGGER%%
This returns the name of the file placed in the FTP folder.
Prefixes, suffixes, and/or file extensions are not allowed. File extensions are not read by the automation engine, so any characters that follow the final dot [.] in a filename are automatically excised