"Hello! I am Elsa."
Translation:Terve! Minä olen Elsa.
Turku/other southwest dialects stretch some final vowels, so you get mää/sää/hää (for minä/sinä/hän), for example.
I agree it's better to start with standard Finnish. Maybe later expansions can add more puhekieli grammar ("mä oon" etc.). Some puhekieli vocabulary is already included right from the start, I've seen "kiitti" and "futis" for example, which are distinctly puhekieli.
'minä' is the singular nominative form of the pronoun, which can be the subject - also, 'olen' is the first-person singular indicative present form of 'olla' (to be) so the original sentence literally means 'I am Elsa.'
And 'my name is ...' would be 'minun nimi on ...' with
- 'minun,' - the genitive singular form of 'minä,'
- 'nimi' - name,
- and 'on' - the third-person present singular form of 'olla.'
(Finnish pronouns are declinable.)
Well, the written Finnish version for "my name is" would actually be "minun nimeni on" with the "-ni" ending in "nimi" to indicate possession (the "minun" wich also indicates possession, could therefore just be left out, as in "nimeni on" (my name is).
In spoken Finnish people would be more likely to use just "nimi", though, e.g. "mun nimi on".
As for rules, well... just ease of speech, I guess. In this case the first letters/sounds and the last "n" are the most important.
(mine, my) "minun" - "mun"
(yours, your) "sinun" - "sun"
(her/his) "hänen" - "sen"
(its) "sen" - "sen"
(ours, our) "meidän" - "meiän"/"mejjän"
(yours, your) "teidän" - "teiän"/"tejjän"
(theirs, their) "heidän" - "niien" ("niiden")
(theirs, their) "niiden" - "niien" ("niiden")
Spoken Finnish has some rules but doesn't always follow them. Chilipalko gives some good examples, but the precise forms are dialectal and how much one's speech changes between the standard Finnish and their regional spoken Finnish also varies by person and by how formally or informally that person is speaking in that context.
Are you on mobile or desktop? On mobile you can hold down letters to get the versions with accents on them. If you're on a laptop or a PC you should be able to add that language to the settings for your keyboard and those accented letters will replace a couple of the keys. (On the Finnish keyboard, the two keys follow along from the second row of letters, going l, ö, ä.)