Only in the absolute spelling (fixed Do) the syllables doremi are corresponding to the cdefg.
But in the relative spelling this tetrad c-eb-gb-bb is the VIIdim of Db (major or minor) and will be spelled ti-re-fa-le (or: se,ti,re,fa,le in Db-minor).
The seven syllables normally used for this practice in English-speaking countries are: do, re, mi, fa, sol, la, and ti (with sharpened notes of di, ri, fi, si, li and flattened notes of te, le, se, me, ra).
Tonic sol-fa (or tonic sol-fah) is a pedagogical technique for teaching sight-singing, invented by Sarah Ann Glover (1785–1867) of Norwich, England and popularised by John Curwen who adapted it from a number of earlier musical systems. It uses a system of musical notation based on movable do solfège, whereby every tone is given a name according to its relationship with other tones in the key: the usual staff notation is replaced with anglicized solfège syllables (e.g. do, re, mi, fa, sol, la, ti, do) or their abbreviations (d, r, m, f, s, l, t, d). "Do" is chosen to be the tonic of whatever key is being used (thus the terminology moveable Do). The original solfège sequence started with "Ut" which later became "Do".