Give your child clues about which rhyming words you are looking for. This game requires some advanced thinking on your child's behalf. For example, you would say: "This farm animal says 'oink' and is big. It is a _______ ." Strive for five successful rhymes with different sentences, and then go for 10.
Read a rhyming book to your preschooler. Instead of completing each sentence, pause and let the child fill in the rhyming word. It is OK if he is not able to provide the exact word, but encourage him if he can at least offer a word that has a rhyming sound. Silly rhyming words are often the most fun. For example, in "Green Eggs and Ham," by Dr. Seuss, you would read: "I do not like green eggs and ham. I do not like them ______ I am." The correct answer for this would be the name "Sam," but if your child says "Pam" or "Gram," accept the answer because she evidently understands the point.
Sing the rhyming name game over and over. This is fun if you have a group or class of children. You can go around the room and choose different names to focus on. You are likely familiar with the rhyme -- just be sure you change the name:
Matt, Matt
Bo bat
Banana, fana, fo, fatt
Me, my, mo Matt...
Matt
Or for a girl's name:
Jenna, Jenna
Bo benna
Banana, fana, fo, fenna
Me, my, mo, menna...
Jenna
Say words in groups of three. If the words all rhyme, have the child put her thumb up. If the words don't all rhyme, have the child put her thumb down and explain which word doesn't fit in. "Glad, sad and mad" all rhyme, so that would be a thumbs-up grouping. "Hit, sit and dog" would get a thumbs-down.