Not schizophrenia (though hallucinations are one feature of schizophrenia). The diagnostic criteria for schizophrenia from DSM-5 are:

A. Two (or more) of the following, each present for a significant portion of time during a 1 -month period (or less if successfully treated). At least one of these must be (1), (2), or (3):

1. Delusions.

2. Hallucinations.

3. Disorganized speech (e.g., frequent derailment or incoherence).

4. Grossly disorganized or catatonic behavior.

5. Negative symptoms (i.e., diminished emotional expression or avolition).

B. For a significant portion of the time since the onset of the disturbance, level of functioning in one or more major areas, such as work, interpersonal relations, or self-care, is markedly below the level achieved prior to the onset (or when the onset is in childhood or adolescence, there is failure to achieve expected level of interpersonal, academic, or occupational functioning).

C. Continuous signs of the disturbance persist for at least 6 months. This 6-month period must include at least 1 month of symptoms (or less if successfully treated) that meet Criterion A (i.e., active-phase symptoms) and may include periods of prodromal or residual symptoms. During these prodromal or residual periods, the signs of the disturbance may be manifested by only negative symptoms or by two or more symptoms listed in Criterion A present in an attenuated form (e.g., odd beliefs, unusual perceptual experiences).

D. Schizoaffective disorder and depressive or bipolar disorder with psychotic features have been ruled out because either 1) no major depressive or manic episodes have occurred concurrently with the active-phase symptoms, or 2) if mood episodes have occurred during active-phase symptoms, they have been present for a minority of the total duration of the active and residual periods of the illness.

E. The disturbance is not attributable to the physiological effects of a substance (e.g., a drug of abuse, a medication) or another medical condition.

F. If there is a history of autism spectrum disorder or a communication disorder of childhood onset, the additional diagnosis of schizophrenia is made only if prominent delusions or hallucinations, in addition to the other required symptoms of schizophrenia, are also present for at least 1 month (or less if successfully treated).

I looked up Dissociative Identity Disorder as well:

A. Disruption of identity characterized by two or more distinct personality states, which may be described in some cultures as an experience of possession. The disruption in identity involves marked discontinuity in sense of self and sense of agency, accompanied by related alterations in affect, behavior, consciousness, memory, perception, cognition, and/or sensory-motor functioning. These signs and symptoms may be observed by others or reported by the individual.

B. Recurrent gaps in the recall of everyday events, important personal information, and/or traumatic events that are inconsistent with ordinary forgetting.

C. The symptoms cause clinically significant distress or impairment in social, occupational, or other important areas of functioning.

D. The disturbance is not a normal part of a broadly accepted cultural or religious practice. Note: In children, the symptoms are not better explained by imaginary playmates or other fantasy play.

E. The symptoms are not attributable to the physiological effects of a substance (e.g., blackouts or chaotic behavior during alcohol intoxication) or another medical condition (e.g., complex partial seizures).

I would be less hesitant to presume this might be the case for some people with tulpas (as a generalization). I doubt many people in the tulpa community would suggest continuing with tulpamancy if a person started to experience symptoms B and C -- though I can imagine it evolving into full-blown Dissociative Identity Disorder if a tulpamancer continued anyways. I do think the tulpa community as a whole (from what I've read) underestimates the dangers of creating a tulpa, but I don't doubt that a significant portion of people could do it healthily and successfully.

I think we need to be careful of connotations and the noncentral fallacy here. Personally, I wouldn't call having a tulpa a "disorder" if the tulpamancer did it on purpose and was in control of the process.

Edit: I would also consider "unusual coping mechanism" a better diagnosis like klkblake mentioned. Again, though, perhaps someone just made a tulpa out of curiosity for fun. Then it wouldn't be a coping mechanism at all. (Edit again: But I forgot about the possibility of "unspecified" like klkblake mentioned and I'd have to pretty much agree with that. This is where my remarks about noncentral fallacy apply.)

There have been a number of reports on the tulpa subreddit from people who have talked to their psychologist about their tulpa. The diagnosis seems to be split 50/50 between "unusual coping mechanism" and "Disassociative Identity Disorder not otherwise specified".