Is is a common practice to do that ? Or should I put informations linked to this input next to it ?
<input type="text" title="You first, not your last name !" placeholder="Name"/>
It's not a common practice, but I think it's not that bad, because in the title, which appears as a tooltip, you give additional information for the user once he enters the field using mouse pointer.
However, I think a better choice would be giving a field a label and use placeholder for descriptive text, so that it looks like:
Name: [ You first, not your last name ]