dt <- data.table(Name =c("A","A","A","A","B","B","B","B","B"),
Number = c(1,3,3,4, 4, 1,1,5,8))
I created cumsum table in this way.
library(matrixStats)
tbl <- round(prop.table(table(dt), 1) * 100, 3)
tbl[] <- rowCumsums(tbl)
names(dimnames(tbl)) <- NULL
tbl[] <- paste0(sub("^([^.]+)(\\.[^0]).*", "\\1\\2", tbl), "%")
cumsumtable <- as.data.frame.matrix(tbl)
In original dt, 2,6 and 7 were missing so it didn't reflect the table.

My desired cumsum table is like this. 2,6 and 7 are filled with the percentage before.

We can convert the 'Number' to factor column with levels specified
dt[, Number := factor(Number, levels = min(Number):max(Number))]
and then running the OP's code
cumsumtable
# 1 2 3 4 5 6 7 8
#A 25% 25% 75% 100% 100% 100% 100% 100%
#B 40% 40% 40% 60% 80% 80% 80% 100%
This can also be done via data.table methods after the column conversion to factor
dcast(dt[, .N,.(Name, Number)][, perc := 100*N/sum(N), Name],
Name ~ Number, value.var = 'perc', fill = 0, drop = FALSE)[,
(2:9) := lapply(Reduce(`+`, .SD, accumulate = TRUE),
function(x) paste0(x, "%")), .SDcols = -1][]
# Name 1 2 3 4 5 6 7 8
#1: A 25% 25% 75% 100% 100% 100% 100% 100%
#2: B 40% 40% 40% 60% 80% 80% 80% 100%
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