They'll be considered the same species. The game is able to keep track of that. (Probably it has an internal ID number for each species, or something of the sort.)
Also, even if name and portrait isn't enough, it is possible to have two starting empires that the game considers the same species. Most easily tested with the two default human empires, but it's not restricted to them. In the starfish stream the game is definitely able to tell that Wiz and Cknoor are playing as the same species. (At one point Wiz noticed that his pops were becoming xenophobic because a foreign empire was oppressing starfish...namely, Cknoor was oppressing his own pops.)