Is it known who replaces whom on SCOTUS if there are two vacancies?

Question

Speculation is that Clarence Thomas may also retire while Republicans hold the Presidency, presumably to ensure his replacement is a Republican-appointed Judge.

Let's assume that happens soon, and there would exist two simultaneous vacancies on SCOTUS, and President nominates two judges to fill those vacancies on the same exact day.

Is there an (1) option or (2) requirement, for him, to spell out specifically which of the two nominees replaces which of the two vacating Judges (assuming neither vacancy is that of Chief Justice)?

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To clarify the question since someone VTCed as "unclear what was asked":

If there are two simultaneous Associate Justice vacancies on the Supreme court and two people being nominated to fill those vacancies by President, is there anything that:

1. Allows the President to specify which of the two nominees is designated for which of the two vacancies?

2. If yes, is there anything that requires the President to do so or is it optional?

Answer 1

TL;DR: President is NOT required to announce who replaces which justice, when more than one Associate Justice vacancy exists.

@Machavity's answer didn't quite answer my question (as his example explicitly didn't count due to involving Chief Justice position, sorry). However, his answer pointed to the Wiki page that did offer one answer; and the correct answer ironically is still Rehnquist related.

Lewis F. Powell Jr. and William Rehnquist were both nominated to the positions of Associate Justice by Nixon on the same day, Oct. 22, 1971; due to vacancies left by Hugo Black and John Marshall Harlan II.

Wikipedia articles for both of these Justices explicitly states that they replaced Black and Harlan respectively (see quotes below):

In 1971, President Richard Nixon appointed Powell to succeed Associate Justice Hugo Black.

In 1971, Nixon nominated Rehnquist to succeed Associate Justice John Marshall Harlan II

However, the primary source for these (Nixon's nominations speech: 337 - Address to the Nation Announcing Intention To Nominate Lewis F. Powell, Jr., and William H. Rehnquist To Be Associate Justices of the Supreme Court of the United States, October 21, 1971) did NOT specify who would replace whom.

It merely mentioned the two Justices who retired, together; and then two Justice nominees. Both were in alphabetical order, so one cannot assume that the order of mentioning them matter.

Answer 2

Ignoring whether it matters, there have been eleven seats on the Supreme Court: the Chief Justice seat (unnumbered); seats 5 and 7 were eliminated; and the seats with the other numbers from 1 to 10.

You can see this on Wikipedia which says:

There are nine seats on the U.S. Supreme Court. When a justice leaves the Court, a replacement is appointed to that same seat. and organized on September 24, 1789 by the Judiciary Act of 1789 1 Stat. 73.
Seat 5 was established on September 24, 1789, by the Judiciary Act of 1789 1 Stat. 73. It was abolished by the Judicial Circuits Act 14 Stat. 209 on July 5, 1867, before the court established the practice of hiring law clerks.
Seat 6 was established on February 24, 1807 by the Seventh Circuit Act 2 Stat. 420.
Seats 7 and 8 were established on March 3, 1837, by the Eighth and Ninth Circuits Act 5 Stat. 176. Seat 7 was abolished by the Judicial Circuits Act 14 Stat. 209 on July 23, 1866, before the court established the practice of hiring law clerks.
Seat 9 was established on March 3, 1863 by the Tenth Circuit Act 12 Stat. 794.
Seat 10 was established on April 10, 1869 by the Circuit Judges Act of 1869 16 Stat. 44.

I would assume that "and organized" should be "as organized".

Anyway, each nominee is appointed to a specific seat, not just to the Supreme Court. E.g.

• Lewis Powell replaced Hugo Black in seat 4 (now Anthony Kennedy's seat).
• William Rehnquist replaced John Harlan II in seat 9 (Rehnquist was replaced by Antonin Scalia when Rehnquist became Chief Justice and then Scalia was replaced by Neil Gorsuch).

Answer 3

It doesn't really matter.

In the US Supreme Court, there are really only two positions: associate justice, and chief justice. The chief justice sets the agenda, but in the end, has no more voting power than the eight other justices.

So, unless the presidential nomination is for chief justice, it doesn't really matter what order they are appointed in, at least officially. Unofficially, this will determine how long the junior justice has the junior duties, such as opening doors for the others, and a few other menial tasks. Yes, even a supreme court justice is subject to a bit of hazing.

To a slight degree, seniority plays a role in who writes the majority opinion, that will be referenced by lower courts in rulings. However, that opinion must reflect the sentiments of the majority of the court, so even that is at best a minor advantage.

But, once on the court, even a junior justice's vote counts as much as the eight other, regardless of how long they've been on the bench.

Answer 4

Generally speaking, we know who is replacing whom on SCOTUS

This actually happened in 2005. Former justice Sandra Day O'Connor announced her retirement on July 1 of that year and (now Chief Justice) John Roberts was nominated to fill her seat. Chief Justice William Rehnquist died on Sept 3, 2005. Roberts nomination was then withdrawn for O'Connor's seat so he could be nominated for Chief Justice. Had Rehnquist been a regular associate justice the re-nomination would have been unnecessary since his position within the court would have not changed.

Incidentally, Rehnquist was an associate justice on SCOTUS before being nominated for Chief Justice.