How to search filenames by regex with "find"

find /home/test -regextype posix-extended -regex '^.*test\.log\.[0-9]{4}-[0-9]{2}-[0-9]{2}\.zip' -mtime +3

1. -name uses globular expressions, aka wildcards. What you want is -regex
2. To use intervals as you intend, you need to tell find to use Extended Regular Expressions via the -regextype posix-extended flag
3. You need to escape out the periods because in regex a period has the special meaning of any single character. What you want is a literal period denoted by \.
4. To match only those files that are greater than 3 days old, you need to prefix your number with a + as in -mtime +3.

Proof of Concept

$ find . -regextype posix-extended -regex '^.*test\.log\.[0-9]{4}-[0-9]{2}-[0-9]{2}\.zip'
./test.log.1234-12-12.zip