How can I teleport only certain people in Minecraft
If you only want to teleport people who are in a certain group, you can use the new scoreboard command to create a 'group' of people (using teams), and then teleport only that team with this command (targets nearest player in the group specified)
/tp @p[team=<internal group name>,<other params here>] <x> <y> <z>
To set up your groups, you can create a group like this:
/scoreboard teams add <internal group name> <display name>
And then add people to this group like this:
/scoreboard teams join <internal group name> <user name>
The advantage of this system is also that you can use it actually to separate groups in the actual game. The scoreboard command has a feature that means that the display name of a team will be displayed before the actual username, appearing like this in the chat:
[<display name>] <user name>: ...
More info on this system can be found in the wiki page linked above.
Changing the @p in the first command above to a player name will stop it from working, because parameters that are inside the [ and ] will only work for @p, @a, and @r. So you cannot substitute the first command above to /tp <player name>[r=2] <x> <y> <z>. It just won't work.
If you really want to use the r parameter on a single person, try using the above method that uses teams, but only put one person in the team. Here is a quick way to do this. Type these into the command console:
/scoreboard teams add <internal player name> <external player name>
/scoreboard teams join <internal player name> <player name>
And then in the command block, to teleport that person if they are in a radius of 2, you could use:
/tp @p[team=<internal player name>,r=2] <x> <y> <z>
Alternatively, you could just specify the name of the player in the selector. Following the previous example, if you want to teleport a certain person if they are in a radius of 2, you could use:
/tp @p[name=<player name>,r=2] <x> <y> <z>
How about specifying the search center?
/tp @p[x=1234,y=64,z=5678,r=2,name=<player name>] <X> <Y> <Z>
or the shorthand
/tp @p[1234,64,5678,2,name=<player name>] <X> <Y> <Z>
I believe if you don't specify the search center, it uses the position of the command block itself.
(Source: Minecraft Wiki)
To response to OP's edit:
with the other code that uses the @p variable it has the radius right but I can set the name property to no one on the server and it still teleports the closest person (it seems to teleport the closest person if it cant find the name, when I want it to teleport nothing if the name is not found).
No, this doesn't happen to me when I test on 1.5.1.