Thank you for your question. It’s wonderful to hear that your child is going through an important milestone.
In many preschools, children are primarily taught uppercase letters. However, kindergarteners are taught uppercase and lowercase letters simultaneously. Since your daughter is 4 1/2 and is getting for kindergarten soon, I would suggest presenting her name to her both in all uppercase and the first letter in uppercase followed by lowercase letters and ask your daughter which one she would like to learn how to write. Explain to her the difference between the two but don’t know your choice or preference. Let her choose and respond positively to her decision.
I initially taught my second grader how to write his name all in uppercase letters but within a week or two, he figured out the corresponding lowercase letters. Then he started playing with writing his name and wrote it both ways.
Its exciting to see that your child is interested in learning to write her name. If she is in preschool, I would check with her teacher to see what they are encouraging. I would also see how they recommend making the letters. Some schools use block print, others use D'Nealian, and others use the Handwriting Without Tears formations. Its important to use the same type of letters that she will need to know for her own kindergarten class. Have fun practicing the letters really large at first as we have better motor memory for movements in our larger muscles and joints. Try sidewalk chalk, writing on an easel, using a wet paint brush on a chalkboard. Think big movements first and lots of fun!