You would need to consult land records for Sussex Co, DE to tell more certainly.Many land records have been abstracted and published; you can find the abstracts for sale by a web search.Or go to the DE Public Archives in Dover to do the research in the actual records.
The tract might not be an older one.Many tracts with long histories of ownership in Sussex Co. DE did not have names.
But around 1784 the Counties made and surveyed many grants of land, and in the surveys and grants I looked at the tracts had names.These grants and surveyes are in volumes of deeds that have *not* been abstracted (I think vols. 'R' and 'S' if memory serves).There is no tract-name index in Sussex Co. records, but the published abstracts do index tract names where they are given.
The Delaware Archives will not do the research for you, but if you go and look in the deeds indexes for those volumes you may well find that 'Liverpool' was one of the 1780s grants.