2004 Dodge Ram Install New 850 Cca Battery 2500 Pickup 2004 Gage Still

I install a new 850 CCA battery in my 2500 Dodge Ram pickup (2004). My battery gage is still sitting on low and the voltage reading accros the battery terminals is 12.5. But, i do notice that battery gage will go back to normal for a while and then back to low. This back-n-forth continues - so i gues i should go after the alternator? or is there something else i should be looking for?

Thank you