Does it have to be only games or can it be activities?
Game: You can make a Memory game with index cards or something like that. Write or type two pairs of nouns (can be both common and proper) on the cards (like two cards with the word GIRL, then two cards with the word DESK etc.). You can do as many pairs as you want. Then they can take turns flipping cards if they find a pair they keep it, just like the Memory games.
Game: Make a sheet with 4 squares and write or type in the first one a 3, the second one a 4, the third one a 5 and the last one a 6. They sit around the table and take turns rolling a die. If they roll a 3 they get to write a noun with THREE letters in their 3 box, if they roll a 4 they can write a noun with FOUR letters in the 4 box etc. If they roll a 1 or 2 they get a free choice of which box they want to write a word in, it just has to have that same amount of letters (for example if they roll a 1 and want to write the word "cat" it has to be written in the 3 box. You can make a rule that whoever gets say 3 words in each box first wins, something like that.
Game: They can HUNT for nouns in the newspaper and highlight it, then make a list of all the ones they found on a separate sheet of paper putting them in the correct column of either proper or common. They would each get one or two sheets of newspaper to HUNT for them. You could time them for say 10 min. of HUNT time then the reminder of the time for the writing of the nouns in the columns, whoever has the most wins (verify the columns with the actual newspaper).
Activity: Get old magazines and give each group 4 pieces of paper (construction or other) and each will have the titles of Person, Place, Animal, Thing. Then they look through magazines to find pictures that would go on each paper.
Hope these help...