I don't believe you'll be permitted to see the Entity_2.Name without adjusting security or creating another (perhaps non-persistent) entity to replicate the available data.
I would create another Access Rule on Entity_2 for the User user role that allows "Read" access to the "Name" attribute without any x-path constraint. I believe the security rights default to the highest available levels of access. In this way, Users can read all Entity_2 "Name"s but only have your originally specified read/write access to the Entity_2 that they're the owner of.
I would try selecting the datasource for the dropdown to be a microflow. The microflow does not (by default) care about access rules, so you will get all the objects that you want. However I am not sure what they will look like to the end user. They might just see a lot of blank options. If this is try then there is no other way apart from refactoring your application. Perhaps you need to have another copy of Entity2 that is available to all users somehow.
As correctly pointed out by Mathew using a microflow as datasource will not work, as the user can not see the Name.