miRNA_ID to GENE_SYMBOL conversion
For mouse gene names and other details you should refer to the mouse genome informatics database (it is a standard organism-specific database like flybase [Drosophila], SGD [yeast], etc). 

However, it is much better to work with RefSeq IDs. Moreover, miRNAs are seldom referred to, using their gene names. Always stick to the miRNA naming convention that is described in miRbase.

I am not sure what you are actually interested in. If you intend to map miRNAs to their targets then you can use one of the standard gene names along with the RefSeq ID. If you are using miRanda or TargetScan to predict the targets then these programs return different identifiers for the target gene including its official gene name. 

In general, for ID conversion, I would prefer BioMart.