Is Dodoma the name of a person or a place?
Dodoma is officially the current capital of Tanzania, although Dar es Salaam remains the de facto capital.
is the "to" in english not translated?
You can kind of think of it as partially being covered by the verb. Kuja kind of means "come to" and kutoka kind of means "come from".
Ninatoka Dodoma. I come from Dodoma.
Correct, prepositions for proper nouns in Swahili are understood. Another example: Mwanamke anakaa Nairobi (The woman lives "in" Nairobi).
Why is it not Dodomani? Or is the directional -ni only added to nouns, not to names?
Yes. As per the tips, proper nouns are not suffixed by -ni.