So basically I have a male teen sim dating my female teen sim. And I just really dislike his first name because originally he wasn't gonna be the one who dated her. But anyone, so I do know how to change his name but my question is will it cause any errors if I do? Like in her memories of him and stuff?

changing a sim's name through any method would update any character's memories of that sim.

I have not encountered any errors from changing a sim's name.

Here you have the right way to do it, whether it is the first or the last name you need to change:
http://sims.wikia.com/wiki/Game_guide:Changing_names

Be careful to not simply open SimPE and change the first name in the SDSC, that will not completely and safely change it.

Sim Blender and Sim Manipulator will also allow you to change a sim's name. When I tried to use the FFS Lot Debugger (Batbox) to remove extra spaces in the names of some townies in Riverside, the game crashed. I was able to fix the names without any problems when I used the Sim Blender instead.

I would use the Sim Manipulator for it can do both with out the copy first name to last name as the Sim Blender does.
Sim Manipulator has a menu to change the first name and a menu to change the last name and is much easier to use.