This is a thread to establish where we should and should not include company suffixes. They are often part of the company name and, in these cases, shouldn't be removed.

For example, "The Malpaso Company" and "The Mirisch Corporation".

DO INCLUDE
The Malpaso Company
The Mirisch Company/The Mirisch Corporation

DO NOT INCLUDE
Any company name followed by a comma and company suffix.

Any other instances we should include? Please post below.

"Corporation" or Company may also be a key part of the company's name in common usage, rather than simply as a designator of its official legal (business) status.

Leading articles (such as "The") and suffixes (such as Company, Corporation, International, Group, etc) are an integral part of the company name and should be included as specified by the company.

The following names specified by the company in film/media credits should be included (and NOT truncated in accordance with the rules for studio/company names):

INCLUDE:
- Australian Broadcasting Corporation (aka ABC)
- British Broadcasting Corporation (aka BBC)
- British Lion Film Corporation

- Columbia Pictures Corporation (1924-1968, replaced by Columbia Pictures Industries, Inc.)
- The Ladd Company
- The Malpaso Company

- The Mirisch Corporation
- The Mirisch Company
- Motion Pictures Corporation of America

- National Broadcasting Company (aka NBC)
- Norway Corporation
- The Walt Disney Company

- Twentieth Century-Fox Film Corporation (1935-1985, informally referred to as "Twentieth Century-Fox")
- Twentieth Century Fox Film Corporation (1985-, informally referred to as "Twentieth Century Fox")


DO NOT INCLUDE
any company name followed by a comma and company suffix.

NOTES:
Truncating to  "Twentieth Century-Fox Film" is meaningless, as no such company name exists.
Same goes for the ABC and BBC, drop "Corporation" and you lose the identity of the company name.

After checking company records, I would have to say no as it will depend on the film's production year.

Clint Eastwood's original "The Malpaso Company" (California jurisdiction) was incorporated in 1967 and dissolved in 1980.

Eastwood's new production company was "Malpaso Productions, Ltd." (California jurisdiction) which was incorporated in 1983 (and is still active).

The rules do not specify just the opening credits, release/production companies can also come from the end credits. In some instances, particularly with more recent films, there are no opening company text credits.