Yesss its true that we can't use the title in BottomApp Bar because it is not convenient in some case where the Floating Button may in Center of BottomApp Bar.
But your problem is genuine, we can't have app bar (even if it is bottom) we need to have a title for that.
Hence I solved it by (old times) compound layout.
<?xml version="1.0" encoding="utf-8"?>
<androidx.coordinatorlayout.widget.CoordinatorLayout xmlns:android="http://schemas.android.com/apk/res/android"
xmlns:app="http://schemas.android.com/apk/res-auto"
xmlns:tools="http://schemas.android.com/tools"
android:layout_width="match_parent"
android:layout_height="match_parent"
tools:context=".MainActivity">
<include layout="@layout/content_main" />
<com.google.android.material.bottomappbar.BottomAppBar
android:id="@+id/bar"
android:layout_width="match_parent"
android:layout_height="wrap_content"
android:layout_gravity="bottom"
app:fabAlignmentMode="end"
app:backgroundTint="@color/colorPrimaryDark">
<!-- Here is the magic happens -->
<RelativeLayout
android:layout_width="match_parent"
android:layout_height="match_parent">
<TextView
android:id="@+id/your_title"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:text="@string/app_name"
android:textColor="#fff"
android:layout_centerInParent="true"
android:textAppearance="@style/Base.TextAppearance.AppCompat.Title"/>
</RelativeLayout>
</com.google.android.material.bottomappbar.BottomAppBar>
<com.google.android.material.floatingactionbutton.FloatingActionButton
android:id="@+id/fab"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
app:layout_anchor="@id/bar"
app:layout_insetEdge="right"
app:rippleColor="@color/colorPrimary"
android:src="@drawable/ic_menu_24"/>
</androidx.coordinatorlayout.widget.CoordinatorLayout>
In above implementation I set the app:fabAlignmentMode="end"
so that we can have neat space for title.
And good thing we this approach is that you can customize your title to any extent using custom fonts, colors.
Output of above implementation :

I hope this solves your problem.