I am reading cel files using affy::readAffy functions. To that purpose, I used a named vector files_URLs (having used GEOquery to retrieve sample information), whose values are full names of the files, and names are the rownames I want to be used for my exprs and phenoData object (using argument sampleNames=names(files_URL)).

Operation is correctly performed (adequate files are read, with names being used for phenodata and exprs matrix as being defined by parameter sampleNames), however, i got following warning message (cf picture) when I perfom following instruction:

raw_object <- affy::ReadAffy (filenames = files_URLs, celfile.path = destdir,  compress = TRUE, sampleNames = names(files_URLs), phenoData = pheno_data,...)

Warning message:
Mismatched phenoData and celfile names!

Please note that the row.names of your phenoData object should be identical to what you get from list.celfiles()!
Otherwise you are responsible for ensuring that the ordering of your phenoData object conforms to the ordering of the celfiles as they are read into the AffyBatch!
If not, errors may result from using the phenoData for subsetting or creating linear models, etc.

all.equal(names(files_URLs), row.names(pheno_data))
[1] TRUE

It would be great that additionally to result of list.celfiles() function, correct ordering could be guessed as well from parameter sampleNames given.

sessionInfo( )

R version 4.0.2 (2020-06-22)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: CentOS Linux 7 (Core)

Matrix products: default
BLAS:   /softhpc/R/4.0.2/lib64/R/lib/libRblas.so
LAPACK: /softhpc/R/4.0.2/lib64/R/lib/libRlapack.so

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C               LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8     LC_MONETARY=en_US.UTF-8   
 [6] LC_MESSAGES=en_US.UTF-8    LC_PAPER=en_US.UTF-8       LC_NAME=C                  LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] bmkanalysis_1.0.0

Pasting a picture of your console rather than the actual output is suboptimal. Why not just copy and paste like you already did with the first part? Anyway, you need to show your work better than that.

> getGEOSuppFiles("GSE23117")
trying URL 'https://ftp.ncbi.nlm.nih.gov/geo/series/GSE23nnn/GSE23117/suppl//GSE23117_RAW.tar?tool=geoquery'
Content type 'application/x-tar' length 73072640 bytes (69.7 MB)
downloaded 69.7 MB

                                                       size isdir mode
C:/Users/jmacdon/Desktop/GSE23117/GSE23117_RAW.tar 73072640 FALSE  666
                                                                 mtime
C:/Users/jmacdon/Desktop/GSE23117/GSE23117_RAW.tar 2020-12-17 09:50:07
                                                                 ctime
C:/Users/jmacdon/Desktop/GSE23117/GSE23117_RAW.tar 2020-12-17 09:50:00
                                                                 atime exe
C:/Users/jmacdon/Desktop/GSE23117/GSE23117_RAW.tar 2020-12-17 09:50:07  no
> setwd("GSE23117/")
> untar("GSE23117_RAW.tar")
> library(affy)
> fn <- dir(".", "CEL.gz")
## reorder to not match output from list.celfiles()
> fn <- fn[sample(1:length(fn), length(fn))]
> all.equal(list.celfiles(), fn)
[1] "13 string mismatches"
## make a phenoData object
> pd <- AnnotatedDataFrame(data.frame(sample = 1:15, row.names = fn))
> pd
An object of class 'AnnotatedDataFrame'
  rowNames: GSM569481.CEL.gz GSM569478.CEL.gz ... GSM569485.CEL.gz (15
    total)
  varLabels: sample
  varMetadata: labelDescription
> z <- ReadAffy(filenames = fn, phenoData = pd)

So it doesn't matter what order you use (list.celfiles is only called if you don't tell ReadAffy which files to read in). But it does matter that the row.names of your phenoData object match the order of the files you read in, which is what the warning is telling you.