Witchipedia

Having a name and birthday help the workings anchor/target the individuals to be affected in the working. Doesn't matter if it's a card reading, love spell or anything else. The work has to have an anchor. If we don't have this information we can use photos, personal items or even bits of that individual like hair, nails and what not. The name and birthday make the casting that much more potent. I'm basing my information purely on my 15 years of experience of working with clients. If there is no specified anchor the casing defaults to the practitioner performing the work. For example, if I were to cast a love spell on a person for a client but don't include the client's identity in some form in my spell the target will fall in love with me. However, visualizations play a huge role in witchcraft, and that image of the target falling in love with the client is one way to include the client in the work using the image of them. I hope this answers the question.

The name and birthdate are used to create a sympathetic link to the target, especially in the absence of a physical object. Spells are cast differently by different witches. Some utilize the aid of spirits. As for conjuring, that depends on your definition. There is a magickal style similar to witchcraft called Conjure, but conjuring in its vernacular involves making something come from nothing, which is not what Witches do.