I managed to set the HC-05 name to "Smartplant" and for a few minutes, the phone found it. (I am using a 4.4.2 version Android.) But now it can't be discovered.
How do I have to connect the module to an Arduino Mega 2560? Do I have to upload some code on the board in order to get access from the phone?
The way I see it there is a two step process for the smart phone and the HC-05. No arduino required for these two steps.
First there is some sort of basic bluetooth protocol level where the phone finds the HC05 and pairs with it. This through the bluetooth settings on the phone, not an app. If unpaired, you should see it as an available device, tap, enter the pin code (1234?) and the HC05 should move from an available device to a paired device. If already paired it will show as a paired device
Once the phone and the module are paired, there is the process of connection to a phone app, like a bluetooth terminal program. I use Kai Morich's Bluetooth Serial Terminal https://play.google.com/store/apps/details?id=de.kai_morich.serial_bluetooth_terminal&hl=en_US
The app should prompt for the connection, show connected, and the light on the module should flash twice every two seconds.
The module should be in normal communications mode not AT mode.
If you want the app to communicate with the Arduino, then software needs to be written for the Arduino to communicate with the bluetooth module over either hardware of software serial.
Can you get the phone paired with the module? Can can you get a terminal program connected to the module?