John E. Alexander, managing director of Off Broadway’s Naked Angels, will exit his post this summer for a gig as exec director of San Diego’s Diversionary Theater.Leadership change coincides with the imminent departure of Naked Angels a.d. Geoffrey Nauffts, whose role will be taken up by current associate a.d. Andy Donald. A search for another managing director is under way. Alexander, who has been with Naked Angels since 2009 and will participate in the search for his replacement, departs in July. In recent seasons, Naked Angels’ producing credits have included “Next Fall,” which went on to have a short Broadway run, and Edie Falco-Alison Pill starrer “This Wide Night,” recently nommed for five Lucille Lortel Awards. More recently, the dropout of a funder for an upcoming production, Bekah Brunstetter’s “A Long and Happy Life,” led to the postponement of the show. Another offering, Zayd Dohrn’s “Outside People,” remains on track for the fall.