Esperanto may or may not "Esperantize" names and proper nouns, depending on many factors. Most standard European names have equivilants, as do many major cities and all nations. Ido, on the other hand, treats most proper nouns as foreign words, and does not render them into Ido.
As stated above, most European given names have Esperanto equivilants: "John" is Johano, "Alexander" is Aleksandro, etc. Because some cultures place the surname first before the given name and others last after it, it is usual in Esperanto circles to find the surname in all capital letters. "John Smith" may be rendered "John SMITH" or "Johano SMITH". Most non-Western names do not have equivilents and are rendered as close as possible in Esperanto orthography.
Ido, on the other hand, simply leaves the names as is; "John Smith" would be "John Smith" in Ido. Names from languages with non-Latin scripts are rendered as phonetically as possible. Ido does not capitalize surnames.
Most countries have their own names in Esperanto. The system of derivation, though is sometimes complex. In Old World nations, where the country is named after an ethnic group, the main root means a person of that group: anglo is an Englishman, franco is a Frenchman. Originally, names of nations were created by the addition of the suffix -ujo (container), hence England and France would be rendered Anglujo and Francujo respectively (literally, "a container full of Englishmen/Frenchmen"). More recently, Esperanto has adopted -io as the national suffix, thus creating names more inline with standard international practice (and less odd-looking): Anglio, Francio.
In the New World, where citizens are named for their nation, the name of the nation is the main word, and its inhabitants are derived from that: Kanado ("Canada"), Kanadano ("Canadian").