For Wendy's, I have seen the sign with W-handshapes starting at the top of the head and then arching downwards to form pigtails.
Friends and I sign "skinny Pepsi" for diet Pepsi. We know there is a "new" sign for diet, but almost all the Deaf here simply fingerspell "diet". But a funny story about "skinny Pepsi".... A deafie asked an interpreter if she wanted "skinny Pepsi" and the interpreter was very puzzled and asked, "skinny Italian???" Deaf explained that some of us use that sign for diet Pepsi.
I have seen a sign developed by local young Deaf for Subway restuarant - and I love this sign. Two C-handshapes wide apart. Left hand close to mouth and right further away. Now pull both hands to left until right hand is close to mouth. Looks like eating a huge sandwich. This sign isn't used by the entire Deaf Community, just some of the young people. Sure wish it would spread!!
There is a Mexican restuarant chain in the Midwest named Taco John's. Friends and I developed our own sign for it - we simply fingerspell T and J at the same time (as in one letter).
For Long John Silver's - I usually see people sign it as long Silver. Some of us sign it as LJS.
There are several signs for McDonalds - the most common I see is MD at the wrist - looks like the same sign for Medical Doctor. I sign it with M-handshapes making the arch, but end it with D-handshapes.