If you have either two owners, or a beneficiary name on the bond, then if one dies the other owns the bond. The difference is that a co-owner has the equal right to cash in the bond at any time. That results in income taxes — see next paragraph.
If you remove your name from a bond it is a taxable event, and it is as if you “cashed” the bond and must pay taxes on all the accumulated interest at your marginal rate. (Note, if you are older that could move you into a higher payment rate for Medicare!)
And a warning; some of the older SERIES EE bonds carry a very high base rate (compared to base rates offered now) and so you really don’t want to cash them in until maturity.
No, you can’t name bonds in your revocable living trust. So if you don’t have a co-owner or beneficiary named, then the bonds become part of your taxable estate, distributed according to your will. (Even if you have a RLT, you should have a ‘pour-over” will for assets like this, and your car, clothing etc, and anything that isn’t titled in the name of your RLT).
To add a beneficiary or co-owner to a savings bond, go to www.TreasuryDirect.gov. here is a direct link to the article that explains how to deal with ownership of savings bonds.