I assume, that you are regularry changing identity (like each 20-50 years - you have to age at the same pace as people around you and if you cannot magically modify yourself, this is how far you can safely go by mundane means), ideally let the old you "die" in an accindent or so to be surely dead, not just missing (still some beleive that Elvis Pressley is alive somewhere else, so he cannot safely re-use his older look and style). That is like 3 identities per century.
Your biggest enemy are ofcource you, as you want to keep some your writings (or writings from your love, or picture or so) and so you came your own bigger museum and you must keep that hidden for all cost. (And you cannot just burn it all, as you need at least something like diary, to remember, who were your enemies, where are dangerous informations about you, where you was too notorius etc. etc.).
Next one are your letters to personal friends/loves, which you gave away - would be wise time to time show your love, that you still keep ALL her letters in one box (and draw her/him to do similar) so you can later easy collect the letters back be it by yourself or by hired burglar, burning donw the whole building or any other means.
The same problem goes for records about you - your friends may draw your pictures, write letters about you to other people, write diaries, all that describing you, sometimes in good details.
Then there are already public materials, like street photo/picture, where you are included, press writing about you, official records (but those are more about your money, houses, nationales etc, so less directly incriminating).
And being immortal, you became too good in some areas, as you have experiences from many lifes. If you would do the same (not recomended), you are too proficient in it ater few centuries of practising it. Doing different things you are skilled in too much areas, which is also hard to hide consistently. So prepare to be little outstanding in each new incarnation - and so more probably noted more than average person - this include more journalist/historican/influent people coverage.
So best you can do is make your personal museum minimalistic and good guarded, burning everything you do not necessery need.
Also the clothes and style changes relatively fast (historicians can from picture/description tell time of origin to like +/- 20 years correct) and there are few different ways at each time, so you will use very distinctive style for one incarnation and totally different for the next one - if you will be portrayed anyway (in pictures or in writings), let it be more about your clothes and extravagacies, then from you are under it. Clothes make a person and it is possible to make so specific impression, that changes to other style nobody would recognise you. (lol, I made it to my wife, I changed and came at her workplace just to be send away by her, cause "there is already after closing time". We where face to face at that moment :) )
What also helps is to make sometimes pause between incarnations (take few years time away), while let other two incarnations overlap - live somewhere as aging and slowing person, many times too lazy/tired to leave house for days, while you make appereance at other place as very active young person - your next incarnation - it would mix your trace.
There will sadly anyway would be some your personal records, but it would be extremely hard to connect them to the same person. So even when there may be here and there some your intimate letter at some museum for everyone to read, nobody would connect it to your other incarnations, mainly the current one.
And you can arrange "dissappearing" of many such letters over years in unrelated cases - like robbing the museum of some special exponates, while making mess all around and let few letters and other small items to be lost too - you do not want to make impression, that only one letter (colection of letters) was stolen - this would make many questions and maybe copies would be studied. But robing it for some historical armor and weapons, or kings crown, or famous jewelry and leave big collateral would give press item to talk about (the main target like jewelry) and ommit all the small collaterals as "and many more priceless items was lost or destroyed" and even if somebody would try make connection, then it would be hard to say, what was really important for you.
Also you need to decide, what is really bothering you (to be deaply personal or too much revealing) and what is better to just leave as not so important (as you do not want to do too many risky moves and leave too many indicies, to someone realize, that ALL letters from THIS and THET person was stolen nearly simulately and start to ask about THOSE personas)