In DNA, the four bases are:
adenine, guanine, thymine, and cytosine.
Each base is attached is attached to a sugar (deoxyribose) to form a nucleoside. Respectively, these are:
adenosine, guanosine, thymidine, and cytidine.
The complete nucleotide consists of the nucleoside attached to a phosphate group. The names of the nucleotides are:
adenylic acid, guanylic acid, thymidylic acid, and cytidylic acid. They can also be named as the radical (adenylate etc.), and all the nucleosides and nucleotides can have "deoxy-" as a prefix to distinguish them from the corresponding forms with ribose (found in RNA).
Another set of names for the nucleotides is adenosine monophosphate (AMP), guanosine monophosphate (GMP) etc. These forms are generally used when describing energy transfer. For example, an additional phosphate added to AMP forms ADP, and a third produces ATP.
In RNA the base thymine does not occur, its place being taken by uracil. The nucleoside is uridine, and the nucleotide uridylic acid.