Yeah, no. When the British or Americans reuse ship names, they do not add a letter or number after the name. The new ship gets a new number, and the number is how they are referred to in flag signals or radio. Battle honors are inherited and accumulate, though.
Just in case someone's interested, here's a list of all the British Invincibles before the 1982 Falklands War one:
1. 3rd rate. Prize taken in 1747. Wrecked in 1758.
2. 3rd rate of 1765. Wrecked in 1801.
3. 3rd rate of 1808. Broken up in 1861.
4. Ironclad of 1869. Later renamed Erebus, c. 1905.
5. Battle cruiser of 1907. Sunk at Jutland in 1916.
Battle honors:
St. Vincent 1780
Chesapeake 1781
St. Kitts 1782
Glorious First of June 1794
Trinidad 1797
Alexandria 1882
Heligoland 1914
Falklands 1914
Jutland 1916
(from Manning, T.D. and Walker, C.F. British Warship Names. London: Putnam, 1959.)