Are we makpid on the decree of Rav Yehudah Hachassid in terms of marriage today? Basically I want to know if my hebrew name is the same as the father of a girl I want to date is that a problem? If it is a problem, what if neither of us go by our hebrew names which avraham but I am called Abe and he is called Alan. And if this is a problem also is there a heter if our middle names are different, I am Avraham Yosef and he is Avraham Shmuel? Is there a problem going out with this girl?

Go out with the girl. The different middle name is sufficient, but even if the names were the same, you could always add a middle name later. Most people are not makpid.