Yes. Generally speaking a creator (i.e. writer, composer, producer, etc.) is only permitted to be an active member of one PRO at a time, however a publisher can belong to multiple PROs at the same time. Having said this, the meaning of the term "music publisher" can be quite different for an individual creator looking to setup their publishing versus a professional 3rd party publishing company that signs and services multiple creators.
If you are an individual creator that also wishes to setup a publisher, there is no requirement for you to have a company or legal entity to setup a publisher with AllTrack, and setting up a publisher with AllTrack does not form a company or legal entity for you. Setting up a publisher with AllTrack simply opens a new publisher account for you that is able to receive the publisher's share of performance royalties. AllTrack creators frequently setup their own publishers with AllTrack for many different reasons which you can read about here.
If however you are an individual that acts as a music publisher for multiple creators, or if you are a professional 3rd party publishing company that represents multiple creators (i.e. controlled writers), in almost all cases you should plan on setting up a publisher at each PRO that your controlled writers are affiliated with. This enables you to receive the publisher's share of performance royalties. It also allows your published creators to list you as the publisher when they are registering songs, or for you to register songs on their behalf, among various other benefits.
Regardless of whether you are an individual AllTrack creator looking to setup your own publisher account or if you are a professional 3rd party publishing company that represents multiple creators, when creating a publisher account at AllTrack you will need to choose a unique industrywide name for it. Unique publisher names are required to avoid confusion in the marketplace when collecting your royalties.
You can perform a new publisher name check here.
You can setup a new publisher account with AllTrack here.