What are the securing rings on the disc brake pads pin called?
Usually it's called a Retaining-Ring, poodle-ring or a split-ring. They will look something like this.



Special pliers are made for their removal and installation, but I usually just use needle-nose pliers.

I'm not familiar with that particular model of caliper, but I do think replacing the ring is probably important. In a pinch, you can tightly wrap and twist a piece of wire in the groove usually occupied by the ring to hold you until you get the right part.

Your local bike shop may have spares specific to that part. You can also try your local hardware store. In the screws and bolts section the will usually have bins of split retaining rings because regardless of the application, when you remove one the "springiness" tends to make them fling off into the tall grass and get lost (at least whenever I do maintenance).