The Different Kinds Of Fashion Jewelry Loops and Clasps

Consulting vendors' offerings and with the very experienced salesmen at my work, I might discover no specific "name" for a locket like you described. Different designs of pendants do integrate a clasp as part of the ornamental lower part but these are not what you are trying to find. These are the "lariat" designs in which one end of the chain is longer than the other, fitting through the shorter end.
My suggestion for a front mounted clasp and pendant:

Any qualified jeweler needs to have the ability to modify a chain to do like you want. The catch to the clasp situation is having an attractive clasp plan so all collaborate to look good on the neck. If looks are trivial, then any sturdy clasp will work, such as a 'lobster claw' or a tough 'spring ring' clasp.
One alternative to the regular clasp styles is the folded metal wire 'hook style' clasp. The wire is bent into a loop so the open end is a little versus the other side, making for a cool friction fit where the pendant loop is moved into. An example of this style is on the following site. Scroll down and on the right side you will see 'NBd109 Aquamarine nugget' in a description. Take a look at the clasp. This is a simple folded wire hook arrangement.
Utilizing this style of clasp, a pendant might be completely connected to one end of the exact same design (with the hook soldered shut) and then the other side may be slid onto the pendant loop to fasten the chain together.
Utilizing jewelry store and Lobster Claw Clasps: These are the typical clasps utilized in necklaces. The lobster claw style transcends in strength.
For clasp like this to work appropriately, the pendant will require a loop going the right instructions. In other words, the front view of the pendant will show the 'looking through the hole' view of the loop on the pendant.
One side of the chain is attached permanently to the loop (left versatile, of course, connected with another loop of metal) and the clasp will be connected to the loop. With the loop on the pendant dealing with as I described, all will hang properly. Obviously, if the loop on the pendant faces the other way, like it would to merely slip over a chain, the pendant will be pulled sideways when the clasp is attached.
As an alternative to altering the loop already on a pendant, an extra loop might be formed and soldered shut, going through the pendant loop. This will give the pendant more 'movement' when used and will look after the instructions issues.
Ask a jewelry expert: As I said previously, any jewelry expert qualified enough to solder sterling silver need to quickly be able to take a chain of nearly any style and modify it to have a 'front' closing clasp which on one method or the other connects to the loop(or loops) of the pendant. The beauty of the total piece will depend on the clasp utilized.
It is possible to utilize two clasps of a decorative style with one on each side of the pendant loop. The hook style clasps work rather well visually however are not as protected as spring loaded types like the lobster claw. Still, jewellery store might be best for appearance sake. These solutions will keep the clasp and the pendant in front without the issue of 'roaming clasps' that end up someplace on the collar bone or so when used.