I need user's user name, but not his password. Should I tell him why I use it I will not want their password, and if yes, should it be a modal or popover?
It's a good idea to guide your users.
Make sure he knows where he is, how he got there and where he can go.
In the example below I've put a 'why we only need your user name' link below the text field. When the user hovers over the text he sees a popup dialog with explanation. The user does not leave the form. The help text is of a lower hierarchy level than the text labels and forms for users who do not need help.
Let your users know why you're collecting data that appears to be abnormal.
When your users sign up, they usually understand that the username and password collected are being used to create an account (which allows them to gain access at any time). But when you start asking for information (putting friction aside) like address during the sign up stage, they might be confused why you need it at that moment in time (as an example). Educate them.
If there is context, more information isn't necessary
If you ask for address while someone is shopping for an item, they might be confused why this is necessary, but if it is asked during the checkout flow, that's when they realize it is needed for shipping purposes.
As for a modal vs popover, that depends on what is on the page. If you're writing a manifesto for the "more information" then a modal might have to suffice, unless there is a lot of space on the page. Keep in mind though, that when you have information that needs to be read, having it in a modal might cause the user to hesitate when reading (WOAH THATS A LOT OF INFORMATION ... CLOSE). Also, showing it on the page itself might shove other important information below, which also adds to the load of information shown all at once.
Be mindful how you convey messages
Don't make it complicated, just tell them in plain language what you're doing. Make it sound vague and it will sound fishy.
The idea of micro interactions
When you're trying to get someone to focus on something, it might be a good idea to just show them that one thing, because cluttering the UI when the user is trying to commit to a certain task will add more of a cognitive load.