Much will depend upon which engine family you're looking for - Windsor, FE, 335, 385, Coyote, SBC, BBC, LSx, etc. The first two are without doubt more prevalent in Cobras than any other engine family, at least in North America. Europe and Australia are different, installing more LSx engines these days, for perhaps no other reason than the abilty to install an emissions-compliant engine.
Regardless, while there are 'big name' shops out there, some of them have reputations among their customers that are less than stellar. Do you want an engine for a car you're going to keep and drive for a long time, or are you looking for one for resale purposes that will 'wow' a buyer? Begin with the end in mind. Uninformed buyers may be wowed by a 'big name' engine, and that may help with resale. If the engine is doing into a 'keeper', then topping my criteria would be a solid, reliable engine builder with many long-term satisified customers. In that regard it would be hard to go wrong with Barry Lykins - active on CC as username blykins.
https://lykinsmotorsports.com/