This is outside the realm of what dynmap is intended to do, I suggest developing an addon to Dynmap that can do this.

We've created a custom faction-like plugin, with 10 different groups/teams. To spice things up we've installed the dynmap plugin and it fully works with the Webregister, making you able to see your own location on the map.

I was wondering if we could make players only see their team/group on the dynmap, including themselves after the Login, but not show the other groups their location?

It should be coded in, I have the same issue