Besides the typical school websites, which do not mention the history behind the naming, I only found an Ancestry.com entry that says J. Allen was born in 1894 to parents Yancy E. Axson and Lillie Axson (Williams). That website also says J. Allen Axson married Agnes Perritt. This seems to be confirmed by another website that says Agnes was born in 1905 and died in 1998 in Jacksonville.
I learned that there's an Axson Street over by the 295 and 10 on the west side, but I am not sure the street is named after J. Allen. I could not find any reason that Yancy Axson was important in Jacksonville, so I assume J. Allen made his way to prominence on his own.
Based on J. Allen's date of birth, I can determine he was not a Confederate soldier. However, he could have fought in WWI. I assume the school probably has information about its namesake that is not shared online.
I am not sure if this Axson family is related to the Axsons of Georgia, but Ellen Axson was Woodrow Wilson's first wife.
Since Agnes passed away fairly recently, I assume someone in Jacksonville knows more about the family and why there's a school named after J. Allen. Go ahead and send me a message if you know more.
[UPDATE]
A reader asked if I'd learned more about J. Allen (I had not), but I decided to give newspaper and other sources online a try. I found a marriage announcement from 1964 that identified the husband as working at J. Allen Axson Elementary School, so I know the school name existed at that point.
I then found the November 1940 Educational Directory Florida. I assumed the Axson search hit was because of the school name, but then I didn't find a school by that name in Duval. What I did find was J. Allen Axson named as the principal of Northeast Springfield Elementary School, which was listed in the White Elementary and High Schools section of the book. (Yes, the directory was even segregated). Axson would have been 46 years old at the time.
When I looked up Northeast Springfield Elementary School, I got to this page, which also named the school J. Allen Axson Elementary School. The current Montessori school of the same name is not the original building, which is located at E17th and Franklin. The building is all boarded up, according to Google Streetview.
The short answer is that Northeast Springfield Elementary 5 was renamed for Principal J. Allen Axson at some point after 1940 and before 1964. The school was eventually abandoned (it looked to be in business in 2010) and the name used for a school built near JTB and Hodges. The photo of the old school identifies it as Public School No 8 above the entrance (not No 5), so I'm not sure about the 5 in the name.
And now J. Allen Axson is the most researched school namesake and principal in all of Jacksonville.
[UPDATE 2]
I used the photo to text tool in Google Photos in order to get the names of the other area principals from 1940. It got most of the school and principal names right, so useful, since I wasn't really planning on typing the list out myself. Anyhow, here are the names of most of the Jacksonville area white schools and principals from back in 1940:
And some of the Negro Elementary and High Schools
Arlington ... Helen Roux
Baldwin ... J.S. Currie
Barker's Camp ... Clementine Days Dennis
Bayard ... Althea McCoy
Benjamin Park ... J.T. Davis
Chaseville ... Aldonia Joyner
College Park ... J.H. Argrett
Cookman ... J.I.E. Scott
Cosmo ... Ruth Solomon
Davis Street ... Isaiah Blocker
Dinsmore ... Ida M. Phillips
East Mayport ... Annie M. Short
Edisto ... Paul Green
Edward Waters ... Howard Gregg
Franklin Street ... W.M. Raines
Greenland ... Amy Smith
Jacksonville Beach ... Priscilla Jones
LaVilla ... Roosevelt D. Madison
LaVilla Park ... Alberta B. Coleman
Lincoln Park ... C.G. Bradham
Lone Star ... Polly Brooks
Long Branch ... James N. Wilson
Mandarin ... Richard Cook
etc.
[UPDATE]
A reader asked if I'd learned more about J. Allen (I had not), but I decided to give newspaper and other sources online a try. I found a marriage announcement from 1964 that identified the husband as working at J. Allen Axson Elementary School, so I know the school name existed at that point.
I then found the November 1940 Educational Directory Florida. I assumed the Axson search hit was because of the school name, but then I didn't find a school by that name in Duval. What I did find was J. Allen Axson named as the principal of Northeast Springfield Elementary School, which was listed in the White Elementary and High Schools section of the book. (Yes, the directory was even segregated). Axson would have been 46 years old at the time.
When I looked up Northeast Springfield Elementary School, I got to this page, which also named the school J. Allen Axson Elementary School. The current Montessori school of the same name is not the original building, which is located at E17th and Franklin. The building is all boarded up, according to Google Streetview.
The short answer is that Northeast Springfield Elementary 5 was renamed for Principal J. Allen Axson at some point after 1940 and before 1964. The school was eventually abandoned (it looked to be in business in 2010) and the name used for a school built near JTB and Hodges. The photo of the old school identifies it as Public School No 8 above the entrance (not No 5), so I'm not sure about the 5 in the name.
And now J. Allen Axson is the most researched school namesake and principal in all of Jacksonville.
[UPDATE 2]
I used the photo to text tool in Google Photos in order to get the names of the other area principals from 1940. It got most of the school and principal names right, so useful, since I wasn't really planning on typing the list out myself. Anyhow, here are the names of most of the Jacksonville area white schools and principals from back in 1940:
DUVAL
Arlington … Ray Owen
Atlantic Beach … Mrs. Edythe DeGrove
Baldwin … Winthrop M. Johnson
Jacksonville Schools
Brentwood … Mrs. Bessie W. Ransom
Central Grammar … Katherine Sproull
Central Riverside … Mrs. Belle Kenniston
Dinsmore … S. N. Snyder
East Jacksonville … Mrs. Marie M. Mott
Fairfield … J. S. Wheatley
Fishweir … Annie McClean
Gorrie, John … W.R. Harden
Grand Park … Major P. Brooke
Hogan-Spring Glen … M.C.Hood Jr.
Jackson, Andrew … M. A. Demorest
Jefferson, Thomas … C. E. Saunders
Kirby-Smith … George F. Siason
Lackawanna … A. K. Roberts
Landon, Juliet … J. L. McCord
Lee, Robert E … J. W. Gilbert
Loretto … C A. McCalley
Murray Hill … Ruth N. Upson
New Springfield … Annie Beaman
Northeast Springfield … J.A. Axson
Norwood … Mrs. Iva T. Sprinkle
Oceanway … N. D Fouraker
Ortega … Mrs. Annie Neighbors
Panama Park … Mr. Lola M. Culver
Pickett … L.C. Wright
Riverside … Mrs Annie L. Housh
Riverview … H.F. Kite
Rutherford, Mattie V. … Nellie Cooke
South Jacksonville … J.C. Fulford
Tenth & Market Sts. … Mrs. Edith B Norris
Wesconnett … C.E. Anderson
etc.
And some of the Negro Elementary and High Schools
Arlington ... Helen Roux
Baldwin ... J.S. Currie
Barker's Camp ... Clementine Days Dennis
Bayard ... Althea McCoy
Benjamin Park ... J.T. Davis
Chaseville ... Aldonia Joyner
College Park ... J.H. Argrett
Cookman ... J.I.E. Scott
Cosmo ... Ruth Solomon
Davis Street ... Isaiah Blocker
Dinsmore ... Ida M. Phillips
East Mayport ... Annie M. Short
Edisto ... Paul Green
Edward Waters ... Howard Gregg
Franklin Street ... W.M. Raines
Greenland ... Amy Smith
Jacksonville Beach ... Priscilla Jones
LaVilla ... Roosevelt D. Madison
LaVilla Park ... Alberta B. Coleman
Lincoln Park ... C.G. Bradham
Lone Star ... Polly Brooks
Long Branch ... James N. Wilson
Mandarin ... Richard Cook
etc.