Include full name string so you can type your name to filter

app/views/cards/assignments/_user.html.erb

@@ -2,6 +2,7 @@
   <%= button_to card_assignments_path(card, params: { assignee_id: user.id }), method: :post,
         class: "popup__btn btn", form_class: "max-width flex-item-grow" do %>
     <span class="overflow-ellipsis flex-item-grow"><%= local_assigns.fetch(:user_label, user.name) %></span>
+    <%= yield if block_given? %>
     <%= icon_tag "check", size: 18, class: "checked flex-item-no-shrink flex-item-justify-end", style: "--icon-size: 1em" %>
   <% end %>
 </li>

app/views/cards/assignments/new.html.erb

@@ -15,7 +15,9 @@
           type: "search", autocorrect: "off", autocomplete: "off", data: { "1p-ignore": "true", filter_target: "input", action: "input->filter#filter" } %>
 
     <ul class="popup__list" data-filter-target="list">
-      <%= render partial: "user", locals: { card: @card, user: Current.user, user_label: "Me" } %>
+      <%= render "user", card: @card, user: Current.user, user_label: "Me" do %>
+        <span class="visually-hidden"><%= Current.user.name %></span>
+      <% end %>
       <%= render collection: @assigned_to, partial: "user", locals: { card: @card } %>
       <%= render collection: @users, partial: "user", locals: { card: @card } %>
     </ul>