[bash] How to use regex in file find

Use -regex:

From the man page:

-regex pattern
       File name matches regular expression pattern.  This is a match on the whole path, not a search.  For example, to match a file named './fubar3',  you  can  use  the
       regular expression '.*bar.' or '.*b.*3', but not 'b.*r3'.

Also, I don't believe find supports regex extensions such as \d. You need to use [0-9].

find . -regex '.*test\.log\.[0-9][0-9][0-9][0-9]-[0-9][0-9]-[0-9][0-9]\.zip'