How do you crochet names?

There are several different ways to crochet names into or onto a crocheted piece. One way would be to finish the piece and cross-stitch the name on it afterwards. This would work best IMO in afghan stitch, but works okay in single crochet as well.

Another way would be to use a different color to make the name stand out. Depending on what you want the back of your work to look like, you can do this in different ways. You would have to either carry your yarn along the back if your color changes are not too far apart, you could work over the second color, always letting the color you are not using sit atop the stitches, or you could cut the yarn at each color change. Those tails would need to either be crocheted over or woven in later.

Yet another method of getting a name in a piece is to work it in filet crochet, using either solid blocks or open blocks for the letters depending on the finished look you desire.

You could also embroider the name - for example if you wanted to "sign" your piece, you could embroider your initials in a corner.

To learn how to work these methods you might consider typing "crochet pictures" into a search engine. There are some who have mastered the techniques and have created great videos to show you how.