These useful informations can be retrieved via direct calls to the ODBC API. This way we don't need DBMS-specific SELECT statement.
External Function Declaration :

FUNCTION integer SQLGetInfo  &
(long hconn, integer infotype, ref string infotypeptr, &
integer bufferlength, ref integer bufferlengthptr) &
LIBRARY "odbc32.dll"

PowerScript:
string ls_dbms, ls_database, ls_user
integer li_length
CONSTANT integer SQL_DBMS_NAME = 17
CONSTANT integer SQL_DATABASE_NAME = 16
CONSTANT integer SQL_USER_NAME = 47
long ll_dbhandle

ls_dbms = space(256)
ls_database = space(256)
ls_user = space(256)
ll_dbhandle = SQLCA.DbHandle()
SQLGetInfo(ll_dbhandle, SQL_DBMS_NAME, ls_dbms, 255, li_length)
SQLGetInfo(ll_dbhandle, SQL_DATABASE_NAME, ls_database, 255, li_length)
SQLGetInfo(ll_dbhandle, SQL_USER_NAME, ls_user, 255, li_length)

MessageBox("Current DBMS" , trim(ls_dbms))
MessageBox("Current DATABASE" , trim(ls_database))
MessageBox("Current USER" , trim(ls_user))