I would keep it as generic as the source.

certificación negativa de nombre : name clearance certificate, perhaps. Business name in the UK would hark back, over 40 years ago, to the London Registry of Business Names for partnerships only and where 'business name searches' could be done in person.

'For deeding purposes' would, as pointed out, refer in the US to dealings in land and 'for indenturing purposes' is more of an employment or 'slave labo/u/r' concept.

Otherwise, 'for purposes of issuing the incorporation papers' would feasibly work Transatlantically.

I like JH's and Adrian's suggestions and I admit I may be "lifting" them somewhat
My understanding comes from this:

COMPANY NAME/LEGAL NAME
Request Criteria

The founding of a company or an institution eligible for entry in the Mercantile Register requires a prior acquisition from the CENTRAL MERCANTILE REGISTER of a favorable certificate which indicates the name under which the company will be identified as an individual subject of the law and obligee in all of its legal relationships.

The first paragraph of Section 413 of the Mercantile Register Regulations currently in effect establishes that "No deed of association may be authorized for any company or other institution eligible for entry, or may its name be modified, unless the Notary is provided with a certificate which establishes that the name selected does not already appear as registered

The name must coincide exactly with the one appearing in the negative certificate issued by the Central Mercantile Register.

The Central Mercantile Register shall have a Section on Company Names which shall be comprised of the followed sections: ( 395 to 397 of the Mercantile Register Regulations )

1º.- Names of companies and other registered institutions.

2º.- Names that are temporarily reserved.

3º.- The names of other organizations whose incorporation has been recorded in other public registers, although they may not be eligible for entry in the Mercantile Register, when so requested by their legitimate representatives.

http://www.rmc.es/DenominacionesSociales.aspx?lang=en

IOW, a prior search certificate showing that the name is not already registered, valid for 3 months, has to be obtained firstly to allow for a company to be rgistered in Spain.

This ref. indeed uses the word "deed" which I believe would not be a propos in the US.

ES: "Esta certificación tendrá una vigencia, **a efectos de otorgamiento de escritura**, de tres meses, contados desde la fecha de su expedición, de conformidad con lo establecido en el artículo 414.1 del Reglamento del Registro Mercantil."

EN: "This certification will be valid, **for the [title] deed authorization purposes**, for three months, starting from its issuance date, in accordance with the stated in Article 414. 1 of the Mercantile Registry Regulations."

Observación 1: Certificación [Certificación de escritura [Certificación de escritura de propiedad]]: Title Deed.

Observación 2: Certificado [Certificado de escritura [Certificado de escritura de propiedad]]: Title Deed.


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Note added at 15 horas (2020-12-31 15:33:45 GMT)
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Modificación:
En lugar de "for the [title] deed authorization purposes" preiero eliminar el articulo "the" y sugerirte la traducción "for [title] deed authorization purposes".
¡Saludos!

I believe that the granting is the issuing or the authorization of a deed, which in legal terms is 'a formal, legal document which is signed, witnessed and delivered to effect a conveyance or a transfer of property, or to create a legal obligation or contract'.