You can change the name of the sublayout item without it affecting things. If you change the actual sublayout ascx file then you need to also change the reference field in the sublayout item but everything else is bound by the id of the item not the name....
save,sitecore,components,sublayout
I'm not sure what the exact issue is with the way you have the control coded currently, I assume is to do with Sitecore control lifescycle so would need more in depth investigation. In any case, I suggest you re-think and implement using a more Sitecore friendly process. Instead you...
To deploy your new sublayout correctly you should create a Sitecore Package. This is basically a zip file that allows you to move both items and disk files between Sitecore instances in a controlled manner. For basic installs of Sitecore, where you have not added any specialised tools, it is...
sitecore,datatemplate,sublayout
When building componentized architectures as you are doing, you will want to implement the datasource property for a sublayout to make your sublayout a datasource-driven sublayout. This article by John West should help on how to set a datasource: http://www.sitecore.net/Learn/Blogs/Technical-Blogs/John-West-Sitecore-Blog/Posts/2010/11/How-to-Apply-Data-Sources-to-Sitecore-ASPNET-Presentation-Components.aspx The basics are: Create a template for your Event to...