When Party P (Plaintiff) files a lawsuit against Party D (Defendant)
and the Defendant submits a motion to dismiss case. Party P submits an
Objection to the motion.
Party D wishes to counter the objection filed by Party P.
Often the document filed opposing a motion is called a "Response" rather than an "Objection" although local practice varies.
A document filed in court address points raised in a "Response" or "Objection" is usually called a "Reply".
So, the person filing the Motion to Dismiss might entitled the document "Reply Regarding Motion to Dismiss" or "Reply to Response To Motion To Dismiss" or "Reply To Objection To Motion To Dismiss".
A reply is usually supposed to be limited to points raised in the response or objection, often has a shorter filing deadline that the original response or objection, and often is subject to a shorter page or word limit in jurisdictions that have them.