Do you have to write out full name for an organization for secondaries?

[Med16484]

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I’m basically mentioning an organization for a few essays for a school. Do I have to write out the entire name every time or can I use a shortened version to save characters? I’ve mentioned the shortened version and longer version in my primary

 

[gyngyn]

A well recognized abbreviation (UCLA, NYU...) need not be spelled out.
Even less well known abbreviations need only be spelled out once. Put the shorter version in after that.