The standard on-hand list (Inventory management > Enquiries and reports > On-hand list) has no ability to search by product dimension name. For instance, if you use color you need to filter on the color codes there is no way to search by color name.
One work around for this is to use Released product variants (Product information management > Products > Released product variants) where you can search by color name. From here under the General tab, you can go to On-hand list. In the header the form displays the Item and DimId you have selected, but it shows the on-hand for all variants, meaning you need to filter again.
The filtering should be based on the Item and DimId in the header.