You pose a excellent question that comes up a lot in practice. Many states have laws in place that forfeit a business entity's existence, list it as expired, or consider it in bad standing when that entity fails to keep up with required state filings or franchise taxes. When this occurs, the laws differ in each state as to the consequences to the particular entity. Some states may consider the entity "involuntarily terminated" whereby the owners must complete a filing to reinstate the entity and pay fees to the state, other states simply require payment of the back taxes or completion of the missing filings. If it appears to be easy enough to reinstate the entity in Kansas, you should probably revive that entity for purposes of continuity and unity of the existing business. This is explained further below.
If you simply file a new LLC in Delaware without reviving the old KS LLC, the new DE LLC will not be the same LLC you operated in Kansas. They will instead be two separate LLCs, and you will have to reconcile ownership of business assets and business contracts with the new LLC. This will be the case regardless of whether you name the DE LLC the same name as the KS LLC, operate the same business through it, or so on. You'll simply end up with all the members of the KS LLC becoming members in a new DE LLC that is a shell company.
What it really sounds like you want to do is to "move" the KS LLC to DE and continue to do business as a Delaware entity. If that is the case, a more effective course of action could be to convert the existing KS LLC into a DE entity ("moving" the entity is sometimes referred to as a "redomestication" of a business, although "conversion" is more technically correct). This process, while not particularly complex, does involve multiple filings in both states and will certainly involve you bringing your KS entity back into good standing. I recommend speaking to an attorney with experience in this business law and who has completed several of these sorts of transactions.
Other things to keep in mind include the fact that: (1) your conversion to a DE entity may affect your existing contracts - have an attorney review any contracts before making the conversion; (2) business entities in DE are subject to a different state-level taxation system than KS, and (3) you will need a registered agent in DE before you can file your DE documents.
Best of luck in your future endeavors!