I'm guessing that you want to be able to change which letter you are searching for in the string, unfortunately couchbase isn't going to be the best thing for this type of query.
If it will always be the letter 'a' that you want to search for then you could do a map like this and then query on the id.
function (doc, meta) {
if(doc.Tenant) {
var name = doc.Tenant.User.Name.toLowerCase();
if(name.indexOf("a") > -1) {
emit(doc.Tenant.Id,null);
}
}
}
If however you want to be able to dynamically change which letter or even substring you want to search for in the name then you want to consider something like elasticsearch (great for text searching). Couchbase has an elasticsearch transport plugin that will automatically replicate to your elasticsearch node(s).
Here is a presentation on ES and Couchbase
http://www.slideshare.net/Couchbase/using-elasticsearch-and-couchbase-together-to-build-large-scale-applications
The documentation for installation and getting started with the ES plugin
http://docs.couchbase.com/couchbase-elastic-search/
And a cool tutorial detailing how to add a GUI on top of your ES data for easy filtering.
http://blog.jeroenreijn.com/2013/07/visitor-analysis-with-couchbase-elasticsearch.html