diff --git a/INSTALL.md b/INSTALL.md
index 2df686b19b07..25343593d529 100644
--- a/INSTALL.md
+++ b/INSTALL.md
@@ -1,3 +1,4 @@
+- [Choosing your server name](#choosing-your-server-name)
 - [Installing Synapse](#installing-synapse)
   - [Installing from source](#installing-from-source)
     - [Platform-Specific Instructions](#platform-specific-instructions)
@@ -10,6 +11,22 @@
   - [Setting up a TURN server](#setting-up-a-turn-server)
   - [URL previews](#url-previews)
 
+# Choosing your server name
+
+It is important to choose the name for your server before you install Synapse,
+because it cannot be changed later.
+
+The server name determines the "domain" part of user-ids for users on your
+server: these will all be of the format `@user:my.domain.name`. It also
+determines how other matrix servers will reach yours for federation.
+
+For a test configuration, set this to the hostname of your server. For a more
+production-ready setup, you will probably want to specify your domain
+(`example.com`) rather than a matrix-specific hostname here (in the same way
+that your email address is probably `user@example.com` rather than
+`user@email.example.com`) - but doing so may require more advanced setup: see
+[Setting up Federation](docs/federate.md).
+
 # Installing Synapse
 
 ## Installing from source
@@ -64,16 +81,7 @@ python -m synapse.app.homeserver \
     --report-stats=[yes|no]
 ```
 
-... substituting an appropriate value for `--server-name`. The server name
-determines the "domain" part of user-ids for users on your server: these will
-all be of the format `@user:my.domain.name`. It also determines how other
-matrix servers will reach yours for Federation. For a test configuration,
-set this to the hostname of your server. For a more production-ready setup, you
-will probably want to specify your domain (`example.com`) rather than a
-matrix-specific hostname here (in the same way that your email address is
-probably `user@example.com` rather than `user@email.example.com`) - but
-doing so may require more advanced setup: see [Setting up Federation](docs/federate.md).
-Beware that the server name cannot be changed later.
+... substituting an appropriate value for `--server-name`.
 
 This command will generate you a config file that you can then customise, but it will
 also generate a set of keys for you. These keys will allow your Home Server to
@@ -86,9 +94,6 @@ different. See the
 [spec](https://matrix.org/docs/spec/server_server/latest.html#retrieving-server-keys)
 for more information on key management.)
 
-You will need to give Synapse a TLS certficate before it will start - see [TLS
-certificates](#tls-certificates).
-
 To actually run your new homeserver, pick a working directory for Synapse to
 run (e.g. `~/synapse`), and::
 
diff --git a/changelog.d/5558.misc b/changelog.d/5558.misc
new file mode 100644
index 000000000000..9ce3555d4559
--- /dev/null
+++ b/changelog.d/5558.misc
@@ -0,0 +1 @@
+Improve install docs on choosing server_name.