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I use the below command to find the file elder than 2 days , it works .

find /var/log -mtime +2 -exec ls -lt {} \;


current result
==============
/var/log/file1
/var/log/file2


But I found that the result is full path , can advise if I want the result is file name only as below , what can i do ?

my desired result
=================
file1
file2

use this:
basename find /var/log -mtime +2 -exec ls -lt {} \;

To format the output of find in various ways, look at using -printf.
find /var/log -mtime +2 -printf '%f\n'

Pipe the result into SED....

eg :

sed 's%^.*/%%'

Replaces any number of characters from the beginning of the line, up to and including the last instance of "/", with an empty character. "%" is used as the delimiter to allow "/" to be in the Regex.

This will do the same thing:
sed 's/^.*\///'