No, there is no prohibition on commercial rental properties treated as a QBI business. If it is a "mixed use" property, you have the choice to treat it as one property or split it into two properties. IRS Revenue Procedure 2019-38 section .04 Rental Services. on page 4 of the PDF at this link provides details about that.
The TurboTax question you are getting to "enter Name and EIN" is not an IRS requirement, it is a TurboTax calculation step. For your situation, you can enter any name in the Name box (e.g., the name you are using for the rental in TurboTax) and leave the EIN box blank.
You may also be interested in this See the IRS article on the rental real estate safe harbor at this link for an overview of the safe harbor requirements.
Lastly, both the Schedule C and the Schedule E you are using are part of a Form 1040 tax return. Schedule C is used to report rental activities when you provide substantial services in conjunction with the property or the rental is part of a trade or business as a real estate dealer. See the section of IRS Publication 527 at this link for more information.
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