Situation 01You are adding a second device to an existing setup
Faster than the first, because the app is installed, you are signed in, and permissions are granted. What remains is pairing, network, name and room.
Same account, same network. The new device must be registered to the same Amazon account as the existing ones, or they will not appear in each other's lists, cannot be grouped, and cannot play audio together. They should also be on the same Wi-Fi network — a device on a guest network or on an extender's separate network may connect fine and still fail to appear alongside the others.
Name it deliberately. By location, in two or three syllables, with no numbers. Kitchen is a good name; Echo Dot 4th Gen stops being true the moment you replace the device. Say the name aloud before committing — it is what you will be saying every day for years.
Names that cause trouble. Anything containing a numeral, because Speaker 2 is ambiguous when spoken. Anything that sounds like another name — Den and Dan's Room will be confused constantly, and so will Study and Studio. Names should differ at the first syllable, not the last.