LED that emits light in different direction
Yes, many, many of them (I see 900 or so individual types in stock at Digikey). 

The naming is not standardized. It could be "right angle" (RA) or "side view" (SV)  or even "side  firing". For example, more-or-less at random, here is a Panasonic one: 



I don't  think the recommended footprints necessarily conform to the standard ones, but some probably do.  

Here's a photo from the catalog showing the way it goes. 



BTW, there  are also LEDs that emit light toward the mounting surface (usually with a protruding lens that fits into a hole in the PCB).