How to get the SQL-server login name of an integrated security account?
To get the AD groups with exsting logins on the instance that your login DC\Somebody belongs to 



xp_logininfo

EXEC xp_logininfo 'DC\Somebody','all';




sys.login_token 

SELECT DISTINCT lt.name 
FROM sys.login_token lt
INNER JOIN  sys.server_principals  sp
ON lt.principal_id = sp.principal_id AND  sp.type != 'R'
WHERE lt.name NOT IN (SELECT name FROM sys.database_principals WHERE type = 'R' AND name IS NOT NULL) 
AND sp.type != 'R';


An example to validate this for other logins with impersonation

EXECUTE AS LOGIN ='DOMAIN\a-rvertongen';

SELECT DISTINCT lt.name 
FROM sys.login_token lt
INNER JOIN  sys.server_principals  sp
ON lt.principal_id = sp.principal_id
WHERE lt.name NOT IN (SELECT name FROM sys.database_principals WHERE type = 'R' AND name IS NOT NULL) 
AND sp.type != 'R';

REVERT;


Result

name
DOMAIN\a-rvertongen
DOMAIN\SERVER_RO
DOMAIN\SERVER_sysadmin
BUILTIN\Administrators





  Also, what happens if multiple groups are added as sql-server logins,
  and I'm a member of them all, and then I login with integrated
  security.Which login will it take ? 


Permissions for multiple AD groups

You will be granted the GRANT / DENY rights of each  AD Group. 
DENY take precedence over GRANT permissions.

A more thorough write up in a previous answer by  @Max Vernon can be found here.