You can set the size of Varnish shared memory log buffer with the
-l shmlogsize parameter:
-l shmlogsize Specify size of shmlog file. Scaling suffixes like 'k', 'm' can be used up to (e)tabytes. Default is 80 Megabytes. Specifying
less than 8 Megabytes is unwise.
You can read about Varnish startup parameters in the official varnishd documentation. Depending on your OS or Linux distribution you will either have to edit the /etc/init.d/varnish script or distribution specific config files (e.g. /etc/default/varnish on Debian).
Bear in mind that writing varnish logs to disk on a high traffic site will eventually produce a large amount of disk I/O, even if you write a huge log buffer every couple of minutes, this will produce load too. If you do not need full logging you can use a daemonized varnishlog process with a filter that selects only the requests you are interested in, thus reducing the need file I/O.