Hi,
I am working here on dependent L permit. I want to know if this is possible.

My dependent L permit (2 years) will expire in february. Since I came here in dependent permit, can i apply for independent (new) L permit under my name again ? (I mean after the allowed 2 years for L Permit.

you can apply but for that you have to deregister your current permit and leave Switzerland while your wp is in process.

Best is to wait for dependent B permit cos its much easier to convert that to WP