Alexander was named by his mother, and I'm guessing she was following human naming conventions since she didn't particularly care about Klingon tradition.
About Romulan names: The character of Valdore (who appeared in ENT) is, in the novels, given the full name of Valdore i'Kaleh tr'Ihaimehn
. Perhaps Romulans follow naming conventions similar to those used in certain Spanish speaking countries, in which a person uses both their mother and father's last names? (for example, the ex-Yankee Bernie Williams, his full name is Bernabé Williams Figueroa)
As for the Jem'Hadar: I heard that Jem'Hadar names are assigned by their First who is the commander of their unit. Is this true? I swear I read that in some novel.