Patronymic names (Russian middle names) are derived from the name of the child's father ("patron"). If the child is a boy, the middle name will end in either -evich, or -ovich. If the child is a girl, the ending will be -ovna, or -evna.
For example, if the child is a boy, and the father's name is 'Aleksandr', then the child's middle name is Aleksandrovich. If the child is a girl, it would be Aleksandrovna. Likewise for the children of 'Sergey', which would be Sergeyevich (boy), and Sergeyevna (girl); or 'Mikhail', which would be Mikhailovich (boy), and Mikhailovna (girl).
Ukrainian middle names function in the same way, with one exception - the female ending is -ivna rather than -ovna/-evna.
Everyone in Russia has a middle name. In a formal situation, Russians are always introduced by their full name, including their patronymic.
Thus, in a formal setting (work colleagues are a very good example of this) you should always address a Russian person by their first name AND their middle name. If your work colleage was "Sergey Mikhailovich Popov", you would address him as "Sergey Mikhailovich". This also applies to anyone older than you that you are not close to.
See the following examples of Russian middle names: