Naming convention of miRNAs
Some general aspects about miRNA nomenclature in addition to canadianer's answer:


mir refers to the pre-miRNA whereas miR refers to the mature form
mir-x-y mir-x-z for example mir-1-1 and mir-1-2 refer to different precursors that give rise to same mature miRNA (i.e. miR-1). These different precursors can be regulated differently. 
The mature miRNA resulting from the 5' arm of the precursor hairpin has a suffix of -5p; similarly the product from the 3' arm has the suffix of -3p. Previously, the lesser expressed/abundant (or unexpressed) of the two products was designated with an asterisk. For e.g. miR-124*. This convention is obsolete now. Any miRNA by default has the -5p/3p suffix. This is useful especially in case of let-7 because there is no uppercase notation to differentiate precursor from the mature miRNA. For example, the mature form is always denoted as hsa-let-7b-5p even though the -3p is never expressed. 
A "family" consists of miRNAs with the same seed sequence (usually 2nd-9th residue). Sometimes it can be observed that one of the arms is less conserved than the other between different precursors. For example in the case of let-7 the -3p(s) do not have a conserved seed sequence, however, all -5p(s) have the same seed sequence. 


And as mentioned in the other answer, the name let-7 just sticks around because of historical reasons.