All the SSRIs and SNRIs will affect sexual function to some extent in a large percentage of users. This is not from any effect they may have on sex hormones, so it will also happen to people on TRT. In some people the side effect go away with time. Others find them positive (for example, they may delay ejaculation, which may be a plus if you have premature ejaculation).
Wellbutrin is said to have less sexual sides but isn't good if you have anxiety, since it is very activating and thus likely to make you more anxious. It's more for people who have the kind of depression that makes them stay in bed sleeping all day.
Remeron is also said to have less sexual side effects but can be very sedating. I haven't seen many positive reviews of Remeron.
Vilazodone is a newer antidepressant that doesn't appear to affect sexual function. It is not an SSRI nor SNRI. (It is said to be an SRI, but that doesn't mean it is necessarily like an SSRI - just as an example, cocaine is also an SRI but is quite different from SSRIs).
A very low dose of amitriptylene, an old tricyclic antidepressant, can be very helpful for sleep and anxiety, without many side effects.