When Japanese people speak to each other, they say ‘Mr.—‘ or ‘Miss.—‘ which is ‘San’ in Japanese. Normally, only after they become very close friends, they stop using ‘San’.
So when Japanese couples become lovers they stop using ‘San’.
If you watch recent Japanese films or TV series, you will see that people don’t normally use their partners names.
Japanese people are not very expressive, even when they are in love. It is not common to call their lover ‘my love’, ‘sweet heart’, etc.
You could call them by their name, like Keiko or Ken, but it is better not to say ‘Anata’. ‘Anata’ is introduced as a translation of ‘you’ in most Japanese text books. However ‘Anata’ sounds very polite and formal, sometimes even bossy. Close Japanese friends never call each other ‘Anata’.
Japanese lovers and couples call each other by their name or nickname. It is very common to call them by their name adding ‘Chan’, especially for ladies (you can also use ‘Chan’ for boys or men as well).
For example, if your girlfriends name is ‘Keiko’ you can call her ‘Keiko-chan’. If ‘Maki’, it would be ‘Maki-chan’. It’s like ‘Xiao-(name)’ in Chinese, ‘A-(name)’ in Cantonese or ‘(name)-chika’ in Russian.
*note; However in some Japanese films and TV, the wives call their husband ‘Anata’, showing their respect, while the husbands never call their wives in the same way. Thinking about my parents, my mother calls her husband (my father) with ‘San’, but my father never does. It is not really the same for younger couples nowadays….