There is no default username and password without you creating one. The simplest possible setup is to follow these steps to set up your own user as a superuser.

At a terminal prompt, create a postgres user with your own username

sudo -u postgres createuser --superuser $USER

Start the postgresql command prompt as your username but running as root since you didn't set a password yet;

sudo -u postgres psql

At the postgresql prompt, set your password;

\password $USER

After that, you should be able to log on just fine.

The setup is more thoroughly documented here.

EDIT:

If you get stuck not being able to authenticate automatically as the postgres user, you may want to compare your /etc/postgresql/9.1/main/pg_hba.conf (ie authentication config file) with the following lines from mine that works; you can get the uncommented ones using

grep -v ^# pg_hba.conf

The "local" lines should be the essential ones in this case since you can't authenticate even from the same machine;

local   all             postgres                                peer
local   all             all                                     peer
host    all             all             127.0.0.1/32            md5
host    all             all             ::1/128                 md5

There are two methods you can use. Both require creating a user and a database.

By default psql connects to the database with the same name as the user. So there is a convention to make that the "user's database". And there isn't any reason to break that convention if your user only needs one database. We'll be using mydatabase as the example database name.

1. Using createuser and createdb, we can be explicit about the database name,

   $ sudo -u postgres createuser -s $USER
   $ createdb mydatabase
   $ psql -d mydatabase
   

   You should probably be omitting that entirely and letting all the commands default to the user's name instead.

   $ sudo -u postgres createuser -s $USER
   $ createdb
   $ psql
   

2. Using the SQL administration commands, and connecting with a password over TCP

   $ sudo -u postgres psql postgres
   

   And, then in the psql shell

   CREATE ROLE myuser LOGIN PASSWORD 'mypass';
   CREATE DATABASE mydatabase WITH OWNER = myuser;
   

   Then you can login,

   $ psql -h localhost -d mydatabase -U myuser -p <port>
   

   If you don't know the port, you can always get it by running the following, as the postgres user,

   SHOW port;
   

   Or,

   $ grep "port =" /etc/postgresql/*/main/postgresql.conf
   

Sidenote: the postgres user

I suggest not modifying the postgres user.

1. It's normally locked from the OS. No one is supposed to "log in" to the operating system as postgres. You're supposed to have root to get to authenticate as postgres.
2. It's normally not password protected and delegates to the host operating system. This is a good thing. This normally means in order to log in as postgres which is the PostgreSQL equivalent of SQL Server's SA, you have to have write-access to the underlying data files. And, that means that you could normally wreck havoc anyway.
3. By keeping this disabled, you remove the risk of a brute-force attack through a named super-user. Concealing and obscuring the name of the superuser has advantages.

When trying to connect via pgadminIII i am prompted for a password when using the same user name.

pgAdminIII is probably connecting over TCP (as opposed to unix domain sockets) and so is subject to the rules of a 'host*' line from pg_hba.conf, rather than a 'local' line. If that line says a password is needed, then it will ask for a password--even if no password is actually assigned to the user. There should be a message in the server log describing the situation in more detail. The details are not sent to the (failed) client, to avoid leaking sensitive information.

Additionally, I would like to make my own user name an admin and use my linux password

It sounds like you might want PAM authentication (or maybe GSSAPI or LDAP). But to use those, you have to change your linux log-on system so that it also uses one of them, as I don't think any of them are configured to do that by default. You can also use peer authentication, which doesn't require your password explicitly, it just uses the fact that you are logged on as the local Linux user (which presumably did require the password) to authenticate to PostgreSQL. Or you could take the easy way out, and just set your PostgreSQL password to be the same thing as your linux password, and then manually keep them in sync.

However when atempting to connect form command line it acts like there should also be a database named the same as my user.

Yes, that is what happens if you don't specify a database name--it assumes you want to connect to a database with the same name as the user. If you want to connect to a different database, then just specify it.

The other answers were not completely satisfying to me. Here's what worked for postgresql-9.1 on Xubuntu 12.04.1 LTS.

1. Connect to the default database with user postgres:

   sudo -u postgres psql template1

2. Set the password for user postgres, then exit psql (Ctrl-D):

   ALTER USER postgres with encrypted password 'xxxxxxx';

3. Edit the pg_hba.conf file:

   sudo vim /etc/postgresql/9.1/main/pg_hba.conf

   and change "peer" to "md5" on the line concerning postgres:

   local      all     postgres     peer md5

   To know what version of postgresql you are running, look for the version folder under /etc/postgresql. Also, you can use Nano or other editor instead of VIM.

4. Restart the database :

   sudo /etc/init.d/postgresql restart

   (Here you can check if it worked with psql -U postgres).

5. Create a user having the same name as you (to find it, you can type whoami):

   sudo createuser -U postgres -d -e -E -l -P -r -s <my_name>

   The options tell postgresql to create a user that can login, create databases, create new roles, is a superuser, and will have an encrypted password. The really important ones are -P -E, so that you're asked to type the password that will be encrypted, and -d so that you can do a createdb.

   Beware of passwords: it will first ask you twice the new password (for the new user), repeated, and then once the postgres password (the one specified on step 2).

6. Again, edit the pg_hba.conf file (see step 3 above), and change "peer" to "md5" on the line concerning "all" other users:

   local      all     all     peer md5

7. Restart (like in step 4), and check that you can login without -U postgres:

   psql template1

   Note that if you do a mere psql, it will fail since it will try to connect you to a default database having the same name as you (i.e. whoami). template1 is the admin database that is here from the start.

8. Now createdb <dbname> should work.