The letters that forms "Rebecca" were just interleaved within the
SRYERBEEACDCIAAEJXFC0 string, as in, letter 2,4,6,8,10,12 and 14. When we extracted them all we were left with just the system name.
In essence we didn't really looked up to the clues to be led toward "ho, there's a relationship with Rebecca there", it just ... popped out
-------------------- Edit ---------------------
To clear things out, nothing in the clues really made us think of Rebecca as such. Sajime happened to play a bit with the string, trying anagrams and whatnot until Lyrae pointed out that not only "Rebecca" could be read within the string with what Sajime had ended up with, but also that the interleaving to get it was exactly every two letters.
Following that we stayed stuck for nearly one day because for some reason we were cutting the string out in separate chunks, as shown below :
http://i.imgur.com/hAM4OoY.png
In the end I tried to recombine the entire string as one while still keeping the "Rebecca" part filtered out, and then pinged the galmap with SYREA, SYREADI, SYREADIA, and finally SYREADIAE, which pinged. As you can see in the above screenshot we also had a few letters wrong or misnoted, and even flipped in the wrong order, but after some poking over different iterations, Jackie Silver got it right.
It was dangerous from us to stick with this theory since we had barely anything to back the "Rebecca" bit up (except that she's the one who spoke to Salomé about the Rift, and who owned the Cobra MKIII that is in the Tionisla Graveyard now, that very one who sent the encoded transmission), but it paid off !