Some Clerky templates that involve the issuance of stock may request that the spouse of the recipient of the shares be included in the transaction. With these templates, the spouse's name is typically used in the spousal consent portion of a stock purchase agreement and in the 83(b) Election form.
In general terms, the principal reason for collecting a spouse’s signature in the spousal consent portion of a stock purchase agreement is to mitigate the risk that a spouse (or, more likely, an ex-spouse) may attempt to assert an interest in the shares and interfere with the terms of their issuance, which can cause a company difficulty.
It is ultimately up to the company to determine whether or not to include a spouse as a party. If a company does not include the spouse, the documents are simply prepared as if the founder is unmarried.
Consult an attorney if you have questions about your specific circumstances.