diff --git a/lib/trinity/scheduler.ex b/lib/trinity/scheduler.ex
index 4cc7b04..f54233d 100644
--- a/lib/trinity/scheduler.ex
+++ b/lib/trinity/scheduler.ex
@@ -50,10 +50,12 @@ defmodule Trinity.Scheduler do
     @type t :: %__MODULE__{
       trap_exit: boolean,
       links: [pid],
+      name_node: atom | nil,
     }
     defstruct [
       trap_exit: false,
       links: [],
+      name_node: nil,
     ]
   end
 
@@ -461,9 +463,22 @@ defmodule Trinity.Scheduler do
       proc_links: proc_links,
       proc_queue_keys: proc_queue_keys,
       proc_nodes: proc_nodes,
+      proc_aliases: proc_aliases,
       node_procs: node_procs,
     } = sim
 
+    # Remove registered name for process
+    case :ets.lookup(proc_links, pid) do
+      [{_key, %ProcInfo{name_node: name_node}}] ->
+        case name_node do
+          {_name, _node} = key ->
+            :ets.delete(proc_aliases, key)
+          nil -> :noop
+        end
+
+      [] -> :noop
+    end
+
     destroy_links(proc_links, pid)
     destroy_proc_node(proc_nodes, node_procs, pid)
     # Note that we do not currently bother to destroy aliases here
diff --git a/lib/trinity/sim_process.ex b/lib/trinity/sim_process.ex
index 28b3285..c2ca1a1 100644
--- a/lib/trinity/sim_process.ex
+++ b/lib/trinity/sim_process.ex
@@ -183,14 +183,21 @@ defmodule Trinity.SimProcess do
   end
 
   defp sim_register(pid, name) do
-    %{proc_aliases: proc_aliases} = get_sim()
+    %{proc_links: proc_links, proc_aliases: proc_aliases} = get_sim()
     node = get_proc_node()
 
+    info =
+      case :ets.lookup(proc_links, pid) do
+        [] -> %ProcInfo{}
+        [{_key, %ProcInfo{} = info}] -> info
+      end
+
     key = {name, node}
-    case :ets.lookup(proc_aliases, key) do
-      [] -> :ets.insert(proc_aliases, {key, pid})
-      [{_key, _pid}] -> raise ArgumentError, "Could not register #{inspect(pid)} with name #{inspect(name)}"
-    end
+    if info.name_node != nil, do: raise(ArgumentError, "Process #{inspect(pid)} already has a name: #{inspect(info.name_node)}")
+    if :ets.member(proc_aliases, key), do: raise(ArgumentError, "Name #{inspect(name)} is already registered on node #{inspect(node)}")
+
+    :ets.insert(proc_aliases, {key, pid})
+    :ets.insert(proc_links, {pid, %{info | name_node: key}})
 
     true
   end