This is the name that appears on your publishing.
You may have heard personal publishing entities referred to as “vanity publishers". In the case where you have a publisher or publishing administrator collecting your publisher’s share on your behalf, having a personal publishing entity is essentially unnecessary in terms of royalty collection, and therefore only acts as an additional publishing company name that appears on your PRO’s website and your royalty statements. Some writers prefer to have that name there, and that’s a personal preference!
Ultimately, creating a personal publishing entity isn’t as complicated as it may seem. It’s mostly up to your personal preference, especially if you have a publisher handling your administration. At the end of the day, having one neither helps nor hurts you, so just be sure to understand what your personal needs are and decide from there.
In short, having your own publishing entity would allow you to have your own publisher name (ex. Emily Mitchell Songs) instead of Songtrust (ex. Songtrust BLVD).