Allow me to play devil's advocate for a moment. Yes, LSU is the flagship university of the state, as per La. R.S. 17:3215, which reads:
"The Louisiana State University system is composed of the institutions under the supervision and management of the Board of Supervisors of Louisiana State University and Agricultural and Mechanical College as follows:
(1) Louisiana State University and Agricultural and Mechanical College, located at Baton Rouge and designated as the premier flagship university for the state.
(2) Repealed by Acts 2011, No. 419, §2, eff. July 12, 2011.
(3) Louisiana State University at Alexandria, located at Chambers.
(4) Louisiana State University at Eunice.
(5) Louisiana State University at Shreveport.
(6) Louisiana State University Health Sciences Center at New Orleans, which shall include medical and related health schools and programs located in New Orleans including those state's medical centers transferred to the Board of Supervisors of Louisiana State University and Agricultural and Mechanical College as provided in Subpart C-2 of Part II of Chapter 4 of this Title, subject to provisions of R.S. 17:1519 et seq.
(7) Louisiana State University Health Sciences Center at Shreveport, which shall include the medical school and related schools at Shreveport, Louisiana State University Hospital at Shreveport, E. A. Conway Medical Center at Monroe, and Huey P. Long Medical Center in Pineville.
(8) The Center for Agricultural Sciences and Rural Development which administers the agricultural extension and research programs of the board throughout the state. The center shall also be responsible for conducting river water research.
(9) Any other college, university, school, institution or program now or hereafter under the supervision and management of the Board of Supervisors of Louisiana State University and Agricultural and Mechanical College."
source:
http://legis.la.gov/lss/lss.asp?doc=80673
Interestingly enough, however, there is no rule I am aware of which prevents the state from having more than one flagship. There are several states which have multiple flagships (e.g., Florida).
As to the name of UL, the only applicable statute is R.S. 17:3217, which reads,
"The University of Louisiana System is composed of the institutions under the supervision and management of the Board of Supervisors for the University of Louisiana System as follows:
(1) Grambling State University at Grambling.
(2) Louisiana Tech University at Ruston.
(3) McNeese State University at Lake Charles.
(4) Nicholls State University at Thibodaux.
(5) Northwestern State University of Louisiana at Natchitoches.
(6) Southeastern Louisiana University at Hammond.
(7) The University of Louisiana at Lafayette.
(8) The University of Louisiana at Monroe.
(9) The University of New Orleans.
(10) Any other college, university, school, institution or program now or hereafter under the supervision and management of the Board of Supervisors for the University of Louisiana System."
Source:
http://legis.la.gov/lss/lss.asp?doc=80675
Neither statute, by the way, says a darn thing about what anyone is required to call either school..... which is why I call the school located in Lafayette "UL," while I call the one in Baton Rouge "that community college 54 miles down I-10 East".