Hello I started therapy and didn´t tell my spouse at first. But I was not feeling well and of course he noticed that but didn´t understand it which did cause problems in daily life. After 3 months in I told him and he is trying to be supportive but we don´t talk about the details. For me it was really hard to tell him but I felt I need his support and being alone in it was hard.
We are honest with each other and trust is a big thing as well and not telling felt wrong to me.

But every relationship is different and especialy if there are problems in the relationship that causing you to go to T in the first place maybe not sharing that is the best choice.
Just don´t push yourself to anything you don´t feel like doing and I wish you best of luck in your therapy.