You are correct, samskrta is to be analysed as containing the prefix sam + past perfect participle krta- from root kr 'to do, to make'.
Probably you are confused by the presence of the -s-.
In modern linguistics, this is called an s-mobile (or mobile-s). It appears only under certain conditions (Cf. samskara-). No fully acceptible explanation has been found for them, but they are a clear feature of Indo-European roots. Other examples include the roots: *teg- 'to cover' beside *steg- (e.g. greek tegos 'roof' and stegu 'cover'. Also sanskrit sthagayati 'he causes to veil').
*pek 'to see' - e.g. skt. pashyati 'he sees' beside *spek, like skt. spash - 'to spy'.
A specialisation in Sanskrit has occured with the combination of sam + kr. It means 'polished' etc.
Of course, in the Sanskrit texts themselves, the most common name for the language is devavani, devabhasya etc meaning 'language of the gods'.
Hope this helps,
Best
Shankar.