The general category of electronic signature products is called “electronic signature” or “e-signature” (acceptable on first reference). “Digital signature” is something different. Don’t use it.
eSignature is the name of a DocuSign product. The “e” is never capitalized, including in a title or at the beginning of a sentence. It’s a noun, never a verb.
eSignature has the same validity as an ink-and-paper signature and should be written about accordingly. Customers use eSignature to sign documents, not “eSignature” or “eSign” them.
After adopting eSignature, the sales team got almost all new contracts signed within one day.
After adopting eSignature, the sales team got almost all new contracts eSigned within one day.