I have used RUVr to remove batch effect in my dataset. Selecting k=10 looks good in my dataset after checking using PCA plots. Now I want to know which estimated factor (W) should be considered in my design matrix for DE analysis?

r <- RUVr(x, gene, k=10,res)

Which W? W-1 or W-10 ?
model.matrix(~ Condition + W)

If you want to use k=10 then you need the first 10 RUV factors. Basically you would combine colData with that matrix that RUVseq returns and then include the columns (=factors) into the design. See for example this analysis from the DESeq2 developer using k=5:

https://github.com/mikelove/preNivolumabOnNivolumab/blob/main/preNivolumabOnNivolumab.Rmd#L112-L144