If you are using the emphatic pattern, which is usual when saying what someone's name, job or role is, the thing being emphasised comes first in the sentence and is followed by ydy/yw:
- Alys yw eich priodfrech. - Alys is your bride.
- Meddyg yw Alys. - Alys is a doctor.
- Chwaer Dewi yw Alys - Alys is Dewi's sister
Mae is used to start a simple, unemphatic sentence:
- Mae Alys yn hoffi nofio. - Alys likes swimming
Ydy? is used to start a simple question:
- Ydy Alys yn hoffi nofio? - Does Alys like swimming?
There are other patterns in which one of mae and ydy/yw is used ratehr than the other - keep looking through the course notes for examples and explanations as you start each new section.
I was just marked wrong for translating Alys to Alice in Welsh to English translation. Yesterday I was marked wrong for not translating Alice to Alys in English to Welsh translation. In my view neither was wrong. Names do not have to be translated. It is a matter of choice for the person.