In the Rabbi Frand tape on choosing Hebrew names, he points to a sefer from only a few hundred years ago that says the Hebrew name shneur was coined when a baby was born; one parent wanted to name the child Meir ("illuminator"), after his/her father; the other parent wanted Yair ("shall illuminate"), after her/his father; they compromised and named the baby shnai-or ("two lights"). But you see that giving two names wasn't common then, or else they could have just called him Meir Yair. (Or Yair Meir ... or maybe they could have, but then they'd fight over who was first? ...)
I recall hearing in yeshiva that the only Rishon with two names is someone in Tosfos called Rabbi Yaakov Yisrael (see Kesubos 98b ד"ה אמר רב פפא). And even then, Yaakov and Yisrael were two names of one person; giving two totally different names was not the fashion a few hundred years ago.
There's the story with Rabbi Akiva Eiger of some child who was having terrible nightmares or something, it turned out he was named after two different grandfathers who had hated each others' guts. Rabbi Eiger went to their graves and demanded they make up with one another; whereupon the child's condition improved.
Lastly, someone asked Rabbi Yaakov Shmuel Weinberg, the late Rosh Yeshiva of Baltimore's Ner Israel:
Rebbe, I hear that if you name the child after two different people, the child will be crazy?
-- Do I look crazy to you?!