When I go travelling, I always buy something small to remember those places such as a keyholder, pottery or little something. When I want to refer to them, which word is appropriate? Can I say, "I bought this as my memory." or "I bought this as a keepsake."? What is the common expression for this?
A common expression is souvenir.
You might say
I bought this as a souvenir of my trip
I bought this as a memory of my trip.
I bought this as a keepsake from my trip.
I bought this as a memento of my trip.
All meaning you have something to remind you of your trip.
They all have the same meaning as 買物 (kaimono), something bought for oneself.
お土産 (omiyage) translates to souvenir, but English does not make this subtle distinction of a souvenir for oneself as opposed to for others.
Having something as a memory can be anything.
Having something as a keepsake usually has some personal and/or emotional connection.
A keepsake is a memory, but a memory is not necessarily a keepsake.
A keepsake is a physical object that is used to help you remember.
A memory is typically a mental process, not a physical object. (Admittedly, M-W's second definition seems like it's referring to a physical object, but my very subjective impression is that it is not a common usage, at least not anymore.)
A keepsake is a physical token that represents to the holder something of meaning to them. A keepsake is kept because of a remembrance. The significance and efficacy of the remembrances are of course symbolic. For the holder the keepsake's function bears more vivid and clear recollection. What is recalled is often their experiences with a person, the meaning those experiences carry. The keepsake could possibly evoke experiences, and the influences of those experiences, with a group of people, an event or a place of significance that carries elements of their own identity and personal recollections' importance.
A keepsake brings to mind circumstances, sentiments, eras, passages of life, concepts, and often characterizations, perceptions, ways of thinking or being, struggles, victories and or moments in some way. In our minds a keepsake can have the effect of drawing our conscience more clearly and vividly to people, times, places, events, and life passages better than a video tape or recording since we can re-experience to some extent the things we recall.
Humans associate objects to feelings events and other objects. This in part defines what it is like to be an alive, thinking and sentient being. The skeletal remains of progenitors represent the living being, the spirit, they once were. Some such objects are keepsakes but only so much as they are of the personal significance.
Even the smallest keepsake can carry a very powerful influence for some but little for others depending on its efficacy or rather strength and clarity of connection they help to be remembered.
A memento may be thought of as a keepsake but is generally more intended to evoke the recollection. For example a plaque or trophy versus a photo of the beach your family visited often throughout your youth.