Try SERVER\SQLEXPRESS (back slash). When I connect to the SQLEXPRESS on my computer I use
If you are connecting to a SQLEXPRESS on another machine then you will have to check that you have been granted access rights for you as currently logged on. If not then access rights will have to be set up (because you are using integrated security). Or you can use a userid/password that has been set up in SQLEXPRESS in which case you will have to specify the userid & password in the connection string.