Limiting it to an individual by name instead of by date means that if he somehow were nominated again in the future, the exception (granted) would apply again. Limitation by date precludes such future [re]application of the exception/law.
And since limitation by date is all that is needed... they probably thought no reason to mention him by name.
As noted in Wikipedia
Since the creation of the position in 1947, such a waiver has only been approved three times, for Army general George Marshall in 1950, Marine Corps General Jim Mattis in 2017, and retired Army general Lloyd J. Austin III in 2021.
And as noted in the comments by CDJB Mattis' exception/law was the first that lacked an explicit name in it (and only relied on dates). There were some concerns raised by Democratic representatives at the time at the time, although not incredibly explicit, possibly because in such a form the law would/ allow a change in the nominee.
For comparison purposes, the S.84 exception for Mattis:
Notwithstanding the second sentence of section 113(a) of title 10, United States Code, the first person
appointed, by and with the advice and consent of the Senate,
as Secretary of Defense after the date of the enactment of this
Act may be a person who is, on the date of appointment, within
seven years after relief, but not within three years after relief,
from active duty as a commissioned officer of a regular component
of the Armed Forces.
(b) LIMITED EXCEPTION.—This section applies only to the first
person appointed as Secretary of Defense as described in subsection
(a) after the date of the enactment of this Act, and to no other
person.
and the one for Austin H.R.335
Notwithstanding the second sentence of section 113(a) of title 10, United States Code, the first person appointed, by and with the advice and consent of the Senate, as Secretary of Defense in an appointment made on or after January 20, 2021, may be a person who is, on the date of appointment, within seven years
after relief, but not within four years after relief, from
active duty as a commissioned officer of a regular component of the Armed Forces.
(b) LIMITED EXCEPTION.—This section applies only to the first person nominated after 12 p.m. (Eastern Standard Time) on January 20, 2021, and appointed as
Secretary of Defense as described in subsection (a), and to no other person.
There is a difference in that the latter law restricts its application to the 1st nomination (not just the 1st appointment) after a certain date. I guess this tightening (appointment-->nomination) may be a result of concerns over the wording of the previous law, but I can't find an explicit discussion.
I also found the exact text authorizing Marshall [H.R. 9646 of 1950], but it's substantially different, not only in that he was named, but also (e.g.) Marshall was an active general at the time and he was given some other exceptions like not taking orders from other military leaders while he was Sec Def, even though he continued to receive pay as an active general as well.
notwithstanding the provisions of section 1222 of the Revised Statutes (U. S. C., title 10, sec. 576), or the proviso contained in section 202 (a) of the
National Security Act of 1947, as amended, or any other provision of
law, the President, acting by and with the advice and consent of
the Senate, is authorized to appoint General of the Army George C.
Marshall to the office of Secretary of Defense and General Marshall's
appointment to, acceptance of, and service in that office shall in no
way affect any status, office, rank, or grade he may occupy or hold
in the Army of the United States or any component thereof, or any
emolument, perquisite, right, privilege, or benefit incident to or arising
out of any such status, office, rank, or grade: Provided, That so long
as he holds the office of Secretary of Defense, General Marshall shall
retain the rank and grade of General of the Army which he now holds
in the Army of the United States and he shall continue to receive the
pay and allowances (including personal money allowance) to which
he is entitled by law, and in the event the salary prescribed by law for
the office of Secretary of Defense exceeds such pay and allowances,
General Marshall shall be authorized to receive the difference between
such pay and allowances and such salary.
SEC. 2. In the performance of his duties as Secretary of Defense,
General Marshall shall be subject to no supervision, control, restriction,
or prohibition (military or otherwise) other than would be operative
with respect to him if he were not an officer of the Army.
SEC. 3. It is hereby expressed as the intent of the Congress that the
authority granted by this Act is not to be construed as approval by
the Congress of continuing appointments of military men to the office
of Secretary of Defense in the future. It is hereby expressed as the
sense of the Congress that after General Marshall leaves the office of
Secretary of Defense, no additional appointments of military men
to that office shall be approved.
The 3rd section had not originated in the Truman proposal itself; it was added by an amendment proposed by Rep. Vinson. The section (since it communicated intent) was described as nonbinding in a 2016 CRS document.
(Interestingly enough, the lack of a 2nd section equivalent from the Marshall law exception was brought up in the Mattis law/exception hearings, because the UCMJ apparently applies to former military personnel as long as they receive a pension.)
As mentioned by Rep. Thornberry and in slighly more detail by Sen. McCain, the language of the resolution was apparently "dictated" by some previously passed "continuing resolution" (passed in Dec 2016, according to Thornberry). McCain said:
before you is a copy of section 179 of the
recently enacted continuing resolution that provides for
expedited consideration of a specifically described bill.
S. 84 is the qualifying legislation prescribed in section
179 as qualifying legislation. S. 84 is entitled to an
expedited procedure that will enable the incoming President
to nominate him, for the Senate to give advice and consent
for General Mattis to serve as Secretary of Defense,
hopefully on the evening of the upcoming inauguration day [...]
In order to avail ourselves of the expedited procedure, the bill may not be amended.
As noted in a CRS report on the matter, the continuing resolution did prescribe most of the text (at least to the extent that it was going to be considered in an expedited hearing)
Both the title of the legislation and the matter after the enacting (or resolving) clause are stipulated.
And the actual prescription is indeed specific like that:
the title of which is as follows: `To provide for an
exception to a limitation against appointment of persons as
Secretary of Defense within seven years of relief from active
duty as a regular commissioned officer of the Armed Forces.';
and
``(3) the matter after the enacting or resolving clause of
which is as follows:
`` `SECTION 1. EXCEPTION TO LIMITATION AGAINST APPOINTMENT OF
PERSONS AS SECRETARY OF DEFENSE
WITHIN SEVEN YEARS OF RELIEF FROM
ACTIVE DUTY AS REGULAR COMMISSIONED
OFFICERS OF THE ARMED FORCES.
`` `(a) In General.--Notwithstanding the second sentence of section
113(a) of title 10, United States Code, the first person appointed, by
and with the advice and consent of the Senate, as Secretary of Defense
after the date of the enactment of this Act may be a person who is, on
the date of appointment, within seven years after relief, but not within
three years after relief, from active duty as a commissioned officer of
a regular component of the Armed Forces.
`` `(b) <<NOTE: Applicability.>> Limited Exception.--This section
applies only to the first person appointed as Secretary of Defense as
described in subsection (a) after the date of the enactment of this Act,
and to no other person.'.
Which, of course, moves the discussion as to why the continuing resolution had this exact text (that later became S.84), but not mentioning a name. It's clear that Mattis was the person being considered even at the time of the adoption of the continuing resolution, because of the specific 3-year "distance" included.
Apparently the inclusion
in an funding bill was so that it could not be easily voted down or filibustered, separately.
Congressional Republicans are using a short-term government funding bill to expedite the nomination of President-elect Donald Trump's pick for Pentagon chief. [...]
Sen. John McCain (R-Ariz.), the Armed Services Committee chairman, also slammed Democrats for threatening to slow walk Mattis.
"If we could get an agreement from them to take up the waiver for Mattis immediately then it wouldn't be necessary, but they haven't given us that assurance, which is disgraceful," he told reporters.
