I just went through a Saints name phase and I wrote down some fun options, maybe some will interest you! I'll try to find one-syllable or J or K names:
Edmund Bryce (or
Brice)
Edmund BlaiseEdmund GeorgeEdmund ClareEdmund GilesEdmund HughEdmund JeanEdmund Jude (cute!)
Edmund Killian (not one-syllable, but one of the few K-names)
Edmund LukeEdmund RochEdmund Cedd
Edmund Yves
There's also some options for place names that are associated with some saints, or their surnames:
Edmund Roye
Edmund JonesEdmund LloydEdmund PayneEdmund StoneEdmund KirbyEdmund Bays
Edmund GwynEdmund WellsEdmund More
Edmund Roe
Edmund Cloyne
Edmund Kolbe
Edmund Kemble
Edmund Kasper