Batch rename objects with number sequence? Is there a way to batch rename objects in a sequence similar to: object1, object2, object3...? Where 'object' would be any custom name?

I found the batch rename datablocks script and it was really helpful for renaming a group of objects but gives a sequence like: object.001, object.002, object.003

Is there any way to use this script to give the first kind of sequence?
import bpy

for i, obj in enumerate(bpy.context.selected_objects, 1):
    bpy.context.scene.objects.active = obj
    obj.name = "object" + str(i)


Just replace "object" with "your name" and run this in the text editor (make sure you have all objects selected that you want renamed).