This is the option I have chosen for my blog. I am extremely fond of the names I've chosen for my children, and I love being able to share things that involve their names. By using their real name I am able to share the story of why we picked the name we did, or I would be able to share any monogrammed projects with ease. Because I love names, this is my favorite option, and I love seeing what names other bloggers have given their children. If Cheri hadn't used her boys' real names, we might not have used Baden for our second son.
All three options are great, use whichever one works best for you on your blog.