Your last sentence indeed resonate as i glance out of my office and see BNY Mellon, UPMC, Highmark etc logos on nearly every landmark building. So not only the naming but quite possibly the design aesthetics would likely have been impacted to work the sponsor logo in visibly. And not just on the CoL but likely every other major campus building. If Pitt were lucky they might be able to contain it to the lawn sign, but there's every possibility that for large enough funding, the sponsor might well insist on a lighted logo right at the top! Can only imagine how it would look...
People don't realize how amazingly ambitious and difficult and unique the Cathedral of Learning project was, on multiple levels. And you have to put into context the state of the university at the time, which was struggling with debt, had a woefully inadequate physical plant, and, institutionally, was pretty much an afterthought locally and nationally. It certainly helped make the university what it is today in a lot of ways by raising its profile and support. It would make for a good Kurlander documentary.
Regarding, the Mellon brothers, they were private donors, so it wasn't from Mellon Bank. Therefore, it probably would have been named like the Pete without a big Mellon bank logo on it.
Here's a breakdown of contributions for the Cathedral of Learning.
Prior to the formal fundraising campaign, the following contributions were received:
Andrew W. & Richard B. Mellon $3,500,000 (the Cathedral lawn land on which it was built, equivalent to a gift of about $51million today). They may have substantially contributed to eliminating the schools $2 million ($29million in today's money) debt as well.
US Steel Co. $325,000 (about $5 million in today's money)
Judge Elbert H. Gary (US Steel Chairman) $50,000
The main fundraising campaign raised $9,178,871 through June 8, 1925. Below are the contributors:
Donors who gave $100,000 to $300,000 (this is like $1.5 to $4.5 million today)
Alcoa
Armstrong Cork
E.V. Babcock
George H. Clapp
Harry W. Croft
Gulf Refining Co.
Heinz Co.
Jones & Laughlin Steel
Koppers Co.
A. Marshall Lockhart
James H. Lockheart
McClintic-Marshall Construction Co.
Philadelphia Company & Affiliated Co.
Hamilton Stewart
J.C. Trees
Weirton Steel Co.
Westinghouse Air Break Co. (specifically $360,000)
Westinghouse Electric Co.
Donors who gave $10,000 to $99,000 (equivalent to ~$150K to $1.5 million today)
Mr. & Mrs. Marcus Aaron
American Window Glass Co.
Christine Arbuckle
James W. Arrott
John F. Casey Co.
George W. Crawford
Arthur V. Davis
Dr. & Mrs. Ogden M. Edwards Jr.
Elliott Company
Leon Falk
Maurice Falk
B.G. Follansbee
Isaac W. Frank
Helen C. Frick
D.L. Gillespie
Gillmore Drug Co.
George B. Gordon
A.R. Hamilton
N. Holmes
A.L. Humphrey
Mrs. Alfred E. Hunt
Roy A. Hunt
Iron City Electric Co.
Annie Given Kerr
H.H. McClintic
H.C. McEldowney
McKenna Brothers
May Drug Co.
W.L. Mellon
Mesta Machine Co.
William L. Monro
Oil Well Supply Co.
E.M. O'Neill
Peoples Natural Gas Co.
Pittsburgh Athletic Association
Mrs. Henry R. Rea
James H. Reed
Reliance Life Insurance Co.
S.S. Robertson
Mr. and Mrs. S. Rosenbloom
Edwin Ruud
Frederic Schaefer
William B. Schiller
Wilson A. Shaw
Malcolm C. Smith
Mrs. W.P. Snyder
W.P. Snyder, Jr.
Spang Chalfant & Co.
Standard Sanitary Manufacturing Co.
Standard Steel Car Co.
Standard Underground Cable Co.
Mrs. Mary R. D. Torrance
Trees Development Co.
United Engineering & Foundry Co.
Vanadium-Alloys Steel Co.
Mrs. H.N. Van Voorhis
E.T. Weir
West Penn Electric Co.
H.D. Williams
Henry Wittmer
Edward A. Woods
In addition, 16,922 individuals and businesses gave gifts of under $10K
97,000 certificates to children for their dimes (~$9,700; or equivalent to about $140K today, so it wasn't a substantial figure in the total cost, but its symbolism was important and it makes for a nice story)
Also, the Banks of Pittsburgh collectively gave $346,260
The Department Stores of Pittsburgh collectively gave $600,000
However, the "tall building" was controversy and let the following sums were removed from the building campaign and placed in the university's endowment:
$600,000 removed by the collective Pittsburgh department stores
$500,000 removed by an unnamed retired business man
$300,000 removed by an unnamed corporation
After the campaign, additional funds were received to finish the Cathedral, which languished during the onset of the depression. The following gifts to finish the building were received.
$10,000 George Gordon (trustee)
$1,030,000 George H. Clapp (that's about a $15 million gift in today's money)
$500,000 A.W. Mellon (stones for the Commons Room, another $7 million gift in today's money)
$500,000 Public Works Administration (workmen wages)
$50,000 E.V. Babcock
$200,000 in additional small checks
This does not count the Nationality Room Committees' fundraising efforts for their individual rooms.
The total cost was somewhere around $15 million by the time it was formally dedicated 1937. But it still could be considered unfinished today.
In addition, the Mellon brothers gave generously to fund the Stephen Foster Memorial. They were big time Pitt benefactors, and remember, Mellon Institute at the time was a defacto division of the University of Pittsburgh, not Carnegie Tech.