Depends on the way you pronounce "u". In Finnish they are nothing alike. "Y" is a front vowel, whereas "u" is a back vowel, that is, they are articulated in the front of and in the back of the mouth, respectively. During wartimes the word "yksi" (one) has for instance been used as a shibboleth to tell apart Finnish and Russian people, since if you pronounced the word as "uksi/juksi" instead of "yksi" it indicated that you were not in fact a native speaker of Finnish. :(
In this context, the meaning is indeed the same, but you would also need to remember that this isn't always the case.
While "I am Pyry" and "My name is Pyry" mean the same thing, something like "Minä olen opettaja/I am a teacher" and "Minun nimeni on opettaja/My name is teacher" obviously don't.