I understand that there is no strict order, but why is it that this specific order is preferable over something like "mihi nomen est" or "nomen tibi est".
The image below is from the Greetings assignment on the Duolingo course for Latin.
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The Latin Duolingo course is not of particularly high quality. Completing the course will certainly give you some insight to Latin, but every detail of the course must be taken with a grain of salt. We have a separate question on the quality of the course.
The words mihi, tibi, ei are the dative forms of the pronouns ego, tu, is/ea/id. Why the dative is used here is best taken to a separate question; like Duolingo, I will not go into it here.
The position of the dative is pretty free and it has the same freedom for all pronouns. The position of est is also not tied to the specific person at all. That is, all these are fine:
Nomen mihi est Marcus.
Nomen tibi est Marcus.
Nomen ei est Marcus.
Mihi nomen est Marcus.
Tibi nomen est Marcus.
Ei nomen est Marcus.
Nomen mihi Marcus est.
Nomen tibi Marcus est.
Nomen ei Marcus est.
Mihi nomen Marcus est.
Tibi nomen Marcus est.
Ei nomen Marcus est.
It is an unfortunate feature of Duolingo — and not just with Latin — that it might get stuck on artificially set phrases and marks some perfectly correct answers as wrong. The freedom of positioning the dative should have been made explicit in the instructions.