You have complicated matters by adding 'Jake'; this appositional expression must itself be separated from the rest of the sentence by commas.
The man who can speak English well is called Jake.
Of those men we are considering, only one speaks English well. He is called Jake.
The man who can speak English well, Jake, works for my brother.
Of those men we are considering, only one speaks English well. That he is called Jake is given as additional information..
That man, who can speak English well, is called Jake.
'Man' is defined by 'that'. The non-defining relative clause simply gives us extra information about him.