You haven't really described why you think the patient has a factitious disorder. But it's great you are thinking about these things! I think a lot of docs just decide something is "psych" without trying to think of what the diagnosis is. However factitious disorder exists on a spectrum of abnormal illness behavior and many people (include most psychiatrists) do not actually seem to understand this, or the difference between the terms.
Factitious Disorder - Falsification of physical or psychological signs or symptoms, or induction of injury or disease, associated with identified deception, in the absence of obvious external rewards
Munchausen's syndrome - Falsification of physical or psychological signs or symptoms, or induction of injury or disease, associated with identified deception, in the absence of obvious external rewards PLUS chronic peregrination (goes from town to town, hospital to hospital, doctor to doctor) and pseudologia fantastica (tells wicked compelling stories that are ridiculous but you really want to believe)
Malingering - Falsification of physical or psychological signs or symptoms, or induction of injury or disease, associated with identified deception, with obvious external reward
Feigning - Falsification of physical or psychological signs or symptoms, or induction of injury or disease, associated with identified deception, where no determination of motivation is made
Elaboration of symptoms for psychological gain - Physical symptoms compatible with and originally due to a confirmed physical disorder, disease, or disability become exaggerated or prolonged due to the psychological state of the patient. An attention-seeking (histrionic) behavioral syndrome develops, which may also contain additional (and usually nonspecific) complaints that are not of physical origin.
Psychosomatic - This really refers to any chronic medical condition in which psychological factors are important. Rheumatoid Arthritis, Crohn's Disease, Asthma, Diabetes, Multiple Sclerosis and so on are all psychosomatic conditions. Not to be confused with somatoform disorders .. Psychosomatic disorders are recognized in DSM-5 by the "psychological factors affecting another medical condition" diagnosis
Somatoform disorders - repeated presentation of physical symptoms, together with persistent requests for medical investigations, in spite of repeated negative findings and reassurances by doctors that the symptoms have no physical basis. c.f. psychosomatic which is often confused with somatoform
Somatization - the use of physical symptoms, often from multiple organ systems as an idiom of distress
Somatization disorder - this was dropped from DSM-5 but refers to individuals with multiple unexplained physical symptoms from 4 different organ systems including pseudoneurological, genitourinary, GI, and musculoskeletal symptoms with recurrent help-seeking behavior
Conversion Disorder - now known as functional neurological disorder (FND), refers to unexplained neurological symptoms. psychological etiology or associated psychosocial factors are no longer necessary or presumed for the diagnosis. It is not a diagnosis of exclusion and should be made on the basis of history and examination identifying physical features compatible with the diagnosis
Compensation neurosis - "Compensation neurosis is a state of mind, born out of fear, kept alive by avarice, stimulated by lawyers, and cured by a verdict". It refers to physical or psychological symptoms that are caused, exaggerated, exacerbated and/or maintained by pending litigation, and where symptoms remit following successful award of damages to the plaintiff.
In practice there is a significant overlap between these different categories. It is not uncommon for factitious disorder patients to be drug-seeking or involved in litigation, but there has to be more to it than that.