[sieve]

A note on the name.

The nasal "m" takes on the form of the nasal in the row/class of the letter that follows it. As "ñ" is the nasal of the "c" class, the "m" becomes "ñ"

Writing Sanskrit terms using the roman script without using something like IAST/ISO-15919 is a pain in the neck. They are going to be mispronounced one way or the other. I try to get the ISO-15919 form and strip away everything that is not a-z.

So, सञ्चिका (sañcikā) = sancika

You probably want to keep the "ch," as the average English speaker is not going to remember that the "c" is the "ch" of "cheese" and not "see."

[arnsholt]

It’s been ages since I did Sanskrit last, but wouldn’t sam-cika typically have the m realized as an anusvara rather than ñ?

[sieve]

Not unless it precedes a classless letter or it is actually "m."

All nasals becoming anusvaras is something Hindi/Marathi and other languages using the Devanagari script do. Sanskrit uses the specific form of the nasal when available.