Potential yuri aside, can the dolls use other guns other than their designation? (New to the series)
Technically you can see instances where like in ST AR-15's MOD 3 she carries an additional SBR. In game I recall HK416 carries a handgun in a thigh holster. In theory story-wise you could swap guns with the dolls back at base maybe by reprogramming them or something. However, having dolls use different guns kind of defeats the purpose of pseudo-anthropomorphize guns since they are named after the gun they use.
Potential yuri aside, can the dolls use other guns other than their designation? (New to the series)
Most certainly, their main gun is the one they're best with because the etching system gives them essentially perfect handling with it. All other guns they can learn to use in a normal way. (This is a plot point for UMP45, and several other dolls have other weapon systems like M4's spoiler cannon, and stuff.)