'Abd = servant
'Abd ul = servant of
Yes. It is common practice to put prefix Abdul- to some of the 99 names of God. Most common are Rahmaan and Raheem which denotes God's attributes of being the Most Compassionate and the Most Merciful.
Other names of God which denote His overwhelming stature and power, like Al-Mutakabbir or Al-Jabbar, are not used, simply out of respect that He alone is fit to wear the names because of His grandeur and magnificence. So you'll almost never hear people with names Abdul Mutakabbir or Abdul Jabbar.
The Prophet used to do this for his companions who had pre-Islamic names which carry bad meanings, he often changed their names to Abdul Rahmaan, e.g. for Abu Hurayrah and Abdul Rahmaan ibn Auf radiyallahu 'anhum (Allah be pleased with them).
Abdullah = servant of Allah = servant of God
Abdul Rahmaan = servant of the Most Compassionate
Abdul Raheem = servant of the Most Merciful