In British English, since does not work in the same way as foreign words often translated as since. I can’t speak for American English, although comments on the question suggest there may be a difference.
Since can indicate either a specific point in the past at which something happened, or a point in the past after which something happened. Which meaning is to be inferred depends on the tense of the accompanying verb. It does not apply to the future; the “something” happened in the past, and although its effect may still pertain, since must apply to the past.
Robusto’s handy aide-memoire chart at How do the tenses and aspects in English correspond temporally to one another? is useful.
My address has changed since March 1.
Your address has changed. It changed at some point in the past. The use of since limits the backward extent of Robusto’s “I have eaten” orange bar: the date it changed was after March 1. It’s perfectly grammatical; but it does not normally mean that you changed your address on March 1:
You wrote to me on March 1 at an address in London; but my address has changed since March 1 and that address is no longer valid.
“My address changed on March 1” means exactly what it says. The date explicitly specifies the date you move house.
I have a new address since March 1.
This is unidiomatic. Since either specifies a point in the past at which something happened, or a point in the past after which something happened. Neither of those can use the present tense, which is the bottom “I eat” line in Robusto’s chart. In this case the idiomatic expression is I have had a new address since March 1: the change took place in the past, on that date.