How to connect wire to multiple part in EAGLE?
All net segments with the same name are connected in Eagle.  If you name a net segment ICSP_DAT by a connector, and then a short segment sticking out from a microcontroller pin also ICSP_DAT, the two will be connected.

Following that logic, each net has exactly one name.  You can't connect two nets by giving segment both names somehow.  If the nets are connected, then they are the same net, so must have the same name.

Of course the other way to connect points of a net is to explicitly wire them together using the NET command.  Implicitly connecting net segments by using names is sometimes referred to as using "air wires".  That can be legitimate to avoid a cluttered ratsnest, and is necessary across pages.  However, you should think carefully about whether directly shown connections might be clearer.

Good schematics aren't only correct, they are clear and easy to interpret correctly by humans.