In the United States, mission selection has always been led by NASA. The methods of selection and appointment evolve over time for past mission a political vocation (willingness to be the first) has missions with scientific purpose (answer the question posed by researchers).
Before the 1980s
The missions were part of a program based on their target:
Explorer and Vandguard: Earth orbit
Ranger and Surveyor: Moon
Pioneer: solar system in general. (mission mentioned here: 10, 11, 12=pioneer venus orbiteur, 13=pioneer venus multiprobe)
missions are named from their design incrementally (mariner 1, 2, 3…) and aim to go ever further (flyby, orbiter, lander).
From the 80s to the 90s
Budgets are allocated to single or double missions with a specific objective and can no longer fit into a program. They therefore often take an individual name that implies that a probe like Magellan or Galileo.
Since the 1990s
Individual missions are federated according to budget categories:
Discovery: cheapest missions (less than 450 million $). Example Stardust, Messenger, Mars insight.
Mars Scout: Discovery sub-program. These are missions low cost (less than $450 million) but exclusively intended for It’s Mars. Phoenix and MAVEN.
Lunar robotic precursor: robotic mission to prepare lunar program inhabited constellation (cancelled in 2010). LRO, LCROSS and LADEE.
New frontier: medium-cost mission (from 450 million to 1 $1 billion). Example, new horizons, juno
Flagship: most expensive mission (over $1 billion). Curiosity and cassini
According to the budget, a number of missions in each category are scheduled. Teams of searchers to present their project to a committee, which selects the mission to based on the scientific priorities allocated by the decade. A once selected, the missions are developed and take on an individual name.
At the beginning of the space area, the USSR faced a reliability problem on their launchers and probes. It therefore mass-produced and launched the probes to compensate for the unreliability. In order to hide these many failures, the missions were given a name only after the launch according to the trajectory followed. For example, a probe destined for Venus was called kosmos in case of failure and Venera if successful. mission numbers are then done incrementally.
Sputnik: the name that means satellite, it meant all probes launched into low orbit from the beginning of the space area.
Kosmos: generic name given to all satellites in orbit or have failed at launch. There are more than 2500 that can be military satellites, non-operational space stations or space probes that have failed to leave Earth’s orbit.
Luna or Lunakoid: scientific exploration of the Moon. Lunakoid uses rovers
Zond: preparation for manned lunar missions but which has also used to hide the failure of probes launched into interplanetary orbit ( mission mentioned here: 1, 2)
From the 80s, the major program Luna , Venera, Mars and Zond are end. the number of missions decreases and moves towards more varying targets. Missions take the name of their target (VEGA, PHOBOS) and sometimes the launch year (MARS 96).
Rest of the world
the other space agency of the world can launch mission but can organize a large exploration program. selection and appointment are only mission-by-mission like NASA in the 1980s and 1990s. Only the European ESA is trying to organize budget categories in the image of NASA at present.