It is common, but not required, to identify the title (and edition) of a diagnostic manual in the text.
You can abbreviate group authors and manual titles in the text but not in the reference list.
See also the guidance on the APA Style website on citing diagnostic manuals: https://apastyle.apa.org/style-grammar-guidelines/references/examples/diagnostic-manual-references
Parenthetical citation (with abbreviation included)
Diagnostic and Statistical Manual of Mental Disorders (5th ed.; DSM-5; American Psychiatric Association, 2013)
International Statistical Classification of Diseases and Related Health Problems (11th ed.; ICD-11; World Health Organization, 2019)
Narrative citation (with abbreviation included)
American Psychiatric Association’s (2013) Diagnostic and Statistical Manual of Mental Disorders (5th ed.; DSM-5)
World Health Organization’s (2019) International Statistical Classification of Diseases and Related Health Problems (11th ed.; ICD-11)
Subsequent parenthetical citations
(American Psychiatric Association, 2013)
Subsequent narrative citations
World Health Organization (2019)
American Psychiatric Association. (2013). Diagnostic and statistical manual of mental disorders (5th ed.).
World Health Organization. (2019). International statistical classification of diseases and related health
problems (11th ed.). https://icd.who.int/
Corporate author. (Date). Title (ed.). DOI or URL