This is normal. Not something to be concerned about. No need to change your alternator
Installing a sound setup means there's extra current draw from your battery. The dimming occurs because there's a lack of current. Step 1 is to make sure you are using good quality wiring for your amp (ofc 8 awg or larger). At the same time, it's best to upgrade your electrical wiring (Big3). A lot of people overlook this and its literally the easiest upgrade. Not only does it eliminate the dimming issue, because you have better current flow between your alt and battery and better grounding, you have less resistance and better flow of current to all your electrical equipment
You can check your battery health but before changing that, just upgrade the 3 wires in your engine bay and watch the magic
