The AP Stylebook and the Merriam-Webster Guide to Punctuation suggest using periods after initials indicating part of a name.
The AP Stylebook specifies that there are no spaces after initials indicating part of a name.
The Merriam-Webster Guide to Punctuation suggests that spaces after the abbreviating periods are permitted when indicating part of a name, but specifies that spaces are not permitted when an entire name is abbreviated.
The AP Stylebook specifies that periods are omitted when an entire name is abbreviated.
The Publication Manual of the APA specifies that periods are omitted for initials in all caps, with the exception of U.S.
Note: Preferences vary. Consult your preferred style guide.