Hi,
Many people use it differently and I don't know what's the proper way.
Suppose you want to write the name with initials of a person called Alfred Brad Chez Dean Eugendis.
Here are three common ways people would write it.
A. B. C. D. Eugendis
A.B.C.D. Eugendis
ABCD Eugendis
What is the proper English way?
When you write the names in full, you leave a space between each one. When you abbreviate a name to just an initial, you are just making the name shorter, which does not change the spacing. The period just represents the missing letters. ie
Alfred Brad Chez Dean Eugendis. = A. B. C. D. Eugendis.
However, in these days where computers are often used to print names, the periods are often omitted.
Best wishes, Clive