They are both correct. The literal spelling of this name is Abd al-Rahman. In the Arabic language if al is followed by an r sound, the al and the r are joined together to form ar. Thus Abd al-Rahman becomes Abd ar-Rahman.
Additionally, the al or ar sound can be joined with the name that precedes it. Thus Abd al-Rahman becomes Abdul Rahman. And this Abd ar-Rahman becomes Abdur Rahman, which can also be written as Abdurrahman.
All of these spellings are acceptable. Abd al-Rahman is closest to how it is written in Arabic, while Abdur Rahman is closest to how it is pronounced in Arabic.
The same applies to other names. For example Abd al-Salam turns to Abdus Salam, both of which are acceptable spellings.