I found a good solution but it is really cumbersome. I use UniProt.ws to derive unique gene names (readable names) and also ambiguous names. I then collapse the columns of unique and ambiguous names into one column, so I have all possible combinations per gene/protein. Later, when I want to integrate with another data set, I separate each possible name into one row so any potential match will work.

data <-  "data/to/protoemics/"

#find gene names corresponding to uniprot ID
library(UniProt.ws)
new_names <- mapUniProt("UniProtKB_AC-ID", "Gene_Name", query =data$UniprotAccession) #unique gene names (Uniprot)
new_names2 <- mapUniProt("UniProtKB_AC-ID", "UniProtKB", query =data$UniprotAccession) #UniProtKB contains a lot of info and multiple protein names
new_names3 <- merge(new_names, new_names2[c("From", "Length","Gene.Names")], by.x = "From", by.y="From")
proteomics_named <- merge(new_names3, data, by.x="From", by.y="UniprotAccession")

# Combining two columns with a space (Gene.Names contains only ambiguous gene names and needs to be combined with the unique gene names columns)
proteomics_named <- proteomics_named %>%
  mutate(Gene.Names = paste(Gene.Names, To, sep = " "))

#now duplicated gene names might occur in the column use this function to clean up
remove_duplicates <- function(text) {
  words <- strsplit(text, " ")[[1]]  # Split the string into words
  unique_words <- unique(words)      # Remove duplicate words
  paste(unique_words, collapse = " ")  # Collapse into a single string
}

# Applying the function to the 'Text' column to remove duplicated names
proteomics_named <- proteomics_named %>%
  mutate(Gene.Names = sapply(Gene.Names, remove_duplicates))

#now separate all gene.names (multiple gene.names per row present) for better merging
proteomics_named <- proteomics_named %>%
  separate_rows(Gene.Names, sep = " ")