How can I log users browsing with there user name ? (instead of ip address)

In the general case - you can't because there is no concept of a username in general browsing.

Now, tell us more about your setup. Does your users log in via your systems? Are you forcing them to use a proxy?

I just want to have proper logs of users browsing, either via Mikrotik web proxy, or route them to SQUID proxy.

Well, unless you force your users to log into a proxy, you can't log usernames - there simply isn't such a concept. If you do force them to log in to the proxy, you should be able to log the usernames, at least with Squid, not sure about MT though.

You can of course do elaborate things to map IP => usernames from logs but that is rarely a simple nor exact way of doing it.