Have a look at Ensembl's Biomart. In attributes, select associated gene name and UniProt/SwissProt ID.

Why don't you use the www.uniprot.org search functionality and using the columns button and download in format tab-delimited to get a list of UniProt Acc\tGene Name? e.g. http://www.uniprot.org/uniprot/?limit=10&force=no&format=tab&columns=id,genes

This you can then use in any tool of your own design.

If you have access to the UniProt blast database you can grab them using blastdbcmd.

A word of caution: UniProt does a good job of standardizing symbols (what you're referring to) as well as short and full names, within UniProt. It can be difficult getting complete mapping if you're using non-standard symbols or naming.

If the use of the UniProt website as proposed above doesn't suit you, you might also consider proceeding as described here.